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NPTEL

Advanced Matrix Theory and Linear Algebra for Engineers

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Comprehensive exploration of advanced linear algebra concepts for engineers, covering vector spaces, transformations, orthogonality, diagonalization, and singular value decomposition.
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40 Lesons
1 day 14 hours
On-Demand
Free-Video

Linear Algebra

1 rewiews
Explore fundamental concepts and techniques of linear algebra, from solving systems to eigenvalues, with emphasis on both theory and practical applications.
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82 Lesons
10 hours
On-Demand
Free-Video

Abstract Algebra

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Explore fundamental concepts of abstract algebra, including groups, rings, fields, and vector spaces, with a focus on definitions, examples, and key theorems.
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33 Lesons
3 hours 30 minutes
On-Demand
Free-Video
NPTEL

Linear Algebra

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In this course, you will learn systems of linear equations, Matrices, Elementary row operations, Row-reduced echelon matrices. Vector spaces, Subspaces, Bases and dimension, Ordered bases and coordinates.
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52 Lesons
1 day 16 hours
On-Demand
Free-Video
NPTEL

Linear Algebra

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The main purpose of this course is the study of linear operators on finite dimensional vector spaces. The idea is to emphasize the simple geometric notions common to many parts of mathematics and its applications.
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60 Lesons
1 day 9 hours
On-Demand
Free-Video
NPTEL

Linear Algebra

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Comprehensive exploration of linear algebra fundamentals, covering matrices, linear systems, vector spaces, transformations, and inner product spaces, with a focus on theoretical concepts and practical applications.
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66 Lesons
1 day 8 hours
On-Demand
Free-Video
NPTEL

Applied Linear Algebra

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Explore vector spaces, linear maps, eigenvalues, and applications in systems, algorithms, and optimization. Gain practical skills in linear algebra for various fields.
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48 Lesons
1 day
On-Demand
Free-Video
Hausdorff Center for Mathematics

A Polynomial Bogolyubov-Type Result for the Special Linear Group

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Explore a mathematical lecture on a polynomial Bogolyubov-type result for the special linear group. Delve into the analogy between subset properties in finite dimensional vector spaces and the special linear group over a finite field. Learn about the ach…
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Institute for Advanced Study

Decoupling Identities and Oriented Matroids and Beyond

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Explore advanced mathematical concepts in decoupling identities and oriented matroids, delving into their applications and extensions in physics and beyond.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video

Vector Spaces

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Explore vector spaces through 25 examples, covering subspaces, unions, spans, and theorems. Delve into dimensions, including infinite ones, and learn about Lagrange Interpolation and Zorn's Lemma.
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14 Lesons
4 hours 30 minutes
On-Demand
Free-Video

Vector Spaces

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Explora espacios vectoriales, subespacios, independencia lineal, coordenadas, bases y dimensiones, y más en este detallado estudio de álgebra lineal.
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15 Lesons
3 hours 30 minutes
On-Demand
Free-Video

Vertex Operator Algebras

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Explore the foundations and applications of vertex algebras, from basic concepts to advanced topics like Heisenberg algebra and permutation orbifolds.
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10 Lesons
5 hours
On-Demand
Free-Video
Kimberly Brehm

Linear Algebra

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Comprehensive exploration of linear algebra concepts, from basic systems to advanced topics like eigenvectors and orthogonal decomposition, with practical applications and problem-solving techniques.
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46 Lesons
11 hours
On-Demand
Free-Video
The Bright Side of Mathematics

Linear Algebra

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Explore vectors, linear combinations, and subspaces in ℝ² and ℝⁿ. Gain a solid foundation in key linear algebra concepts through clear explanations and practical examples.
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7 Lesons
1 hour 30 minutes
On-Demand
Free-Video
The Bright Side of Mathematics

Distribution Theory

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Explore the foundations of distribution theory, covering key concepts from delta functions to coordinate transformations in mathematical analysis.
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9 Lesons
1 hour 30 minutes
On-Demand
Free-Video
Professor Dave Explains

Linear Algebra

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Comprehensive exploration of linear algebra concepts, from matrices and vector spaces to eigenvalues and transformations, with practical applications and in-depth explanations.
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21 Lesons
3 hours 30 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Orthogonality of Signals - Lecture 10

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Explore orthogonality of signals, a fundamental concept in signal processing and communication systems. Gain insights into its applications and importance.
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1 Lesons
16 minutes
On-Demand
Free-Video
Insights into Mathematics

The Algebra of Boole Is Not Boolean Algebra - Math Foundations

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Exploring Boole's original algebra, its connection to Aristotelian logic, and its distinction from modern Boolean algebra. Delves into syllogisms, existential import, and applications in mathematics.
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5 Lesons
27 minutes
On-Demand
Free-Video
Insights into Mathematics

Affine and Projective Geometry, and the Problem of Lines

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Explore affine and projective geometry, focusing on points, vector spaces, and lines in 2D. Learn to solve geometric problems using projective coordinates and understand curve representation.
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9 Lesons
51 minutes
On-Demand
Free-Video
Insights into Mathematics

An Introduction to Abstract Algebra - Abstract Algebra Math Foundations

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Explore fundamental algebraic structures like groups, rings, fields, and vector spaces through intuitive examples, providing a bird's-eye view of abstract algebra's foundational concepts.
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5 Lesons
26 minutes
On-Demand
Free-Video
Ryan O'Donnell

Linear Algebra

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Explore vector spaces, linear combinations, and applications in computer science, including Fibonacci sequences and message transmission on noisy channels.
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11 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Insights into Mathematics

Linear Algebra With Polynomials - Wild Linear Algebra A

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Explore polynomials in linear algebra, covering interpolation, regression, and isomorphism. Learn to apply geometric approaches to transformations and connect polynomial spaces with vector spaces.
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26 Lesons
46 minutes
On-Demand
Free-Video
Insights into Mathematics

The Geometry of a System of Linear Equations - Wild Linear Algebra A

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Explore the geometry of linear equations through a novel approach using properties instead of infinite sets. Gain insights into subspaces, kernel, and linear transformations with practical examples.
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31 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Insights into Mathematics

Rank and Nullity of a Linear Transformation - Wild Linear Algebra A - NJ Wildberger

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Explore linear transformations in higher dimensions, focusing on kernel, image, nullity, and rank. Learn to visualize 4D space and apply row reduction techniques to solve problems.
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19 Lesons
1 hour 1 minute
On-Demand
Free-Video
Insights into Mathematics

An Informal Introduction to Abstract Algebra

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Informal introduction to abstract algebra, covering fields, rings, and vector spaces. Explores key concepts and examples, from basic number systems to advanced constructions, providing essential background for algebraic topology.
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12 Lesons
49 minutes
On-Demand
Free-Video
Insights into Mathematics

Applications of Row Reduction II - Wild Linear Algebra A

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Explore row reduction applications in linear transformations, spanning sets, and linear independence. Gain insights into vector spaces and matrix operations through practical examples and in-depth analysis.
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11 Lesons
57 minutes
On-Demand
Free-Video
Derek Banas

Gram-Schmidt Process in Linear Algebra - Lecture 27

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Learn the Gram-Schmidt Process to transform linearly independent vectors into an orthonormal basis, a crucial technique in linear algebra with applications in various fields of science and engineering.
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1 Lesons
20 minutes
On-Demand
Free-Video
Michael Penn

What Is the Free Vector Space?

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Explore the concept of free vector space through clear definitions, illustrative examples, and practical applications in this concise mathematical tutorial.
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5 Lesons
23 minutes
On-Demand
Free-Video
Michael Penn

The Vector Spaces for Vertex Algebras

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Explore key vector spaces for vertex algebras: polynomial rings, exterior algebras with infinite variables, and universal enveloping algebra of the Virasoro Lie algebra. Gain essential understanding for advanced algebraic studies.
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1 Lesons
21 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Lattice Topological Phases - IPAM at UCLA

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Explore lattice topological phases with Fiona Burnell, covering lattice Hamiltonians, vector spaces, local rules, and gauge choices in this comprehensive lecture on advanced quantum physics concepts.
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14 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

Homological Mirror Symmetry - Categorical Donaldson-Thomas Theory of C^3 and Beyond

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Explore advanced concepts in Donaldson-Thomas theory, including categorifications, refinements, and applications to C^3 and beyond, with a focus on categorical invariants and correspondences.
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14 Lesons
1 hour
On-Demand
Free-Video
Khan Academy

Visualizing a Column Space as a Plane in R3 - Vectors and Spaces - Linear Algebra

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Explore how to visualize column space as a plane in R3, determining planar equations and understanding multi-dimensional concepts in linear algebra.
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1 Lesons
21 minutes
On-Demand
Free-Video
Khan Academy

Null Space and Column Space Basis - Vectors and Spaces - Linear Algebra - Khan Academy

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Learn to determine null space and column space basis for matrices, essential concepts in linear algebra for understanding vector spaces and transformations.
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1 Lesons
25 minutes
On-Demand
Free-Video
Khan Academy

Defining the Angle Between Vectors - Vectors and Spaces - Linear Algebra - Khan Academy

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Learn to define and understand the concept of angles between vectors in linear algebra, enhancing your grasp of vector geometry and spatial relationships.
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1 Lesons
25 minutes
On-Demand
Free-Video
Khan Academy

Linear Subspaces - Vectors and Spaces - Linear Algebra

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Explore linear subspaces in Rn, a fundamental concept in linear algebra. Learn to visualize and understand multi-dimensional mathematical reasoning through vectors, matrices, and transformations.
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1 Lesons
23 minutes
On-Demand
Free-Video
Khan Academy

Parametric Representations of Lines - Vectors and Spaces - Linear Algebra - Khan Academy

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Explore parametric representations of lines in R2 and R3, a fundamental concept in linear algebra. Learn to visualize and understand multi-dimensional mathematical reasoning.
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1 Lesons
25 minutes
On-Demand
Free-Video
Khan Academy

Vector Examples - Vectors and Spaces - Linear Algebra - Khan Academy

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Explore visual understanding of basic vector operations in linear algebra. Learn to visualize and manipulate vectors in multiple dimensions, enhancing your grasp of mathematical concepts.
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1 Lesons
26 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Sanjeevi Krishnan - Homological Programming

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Explore algebraic topology applications in programming, covering pursuit-evasion problems, positive cones, Alexander duality, and directed topology, with insights into decomposability and computational aspects.
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17 Lesons
57 minutes
On-Demand
Free-Video
Khan Academy

Another Example of a Projection Matrix - Linear Algebra - Khan Academy

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Learn to calculate projection matrices by first determining the orthogonal complement's matrix. This advanced linear algebra lesson explores subspace projections and their applications in multidimensional reasoning.
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1 Lesons
22 minutes
On-Demand
Free-Video
Khan Academy

Rowspace and Left Nullspace - Matrix Transformations - Linear Algebra - Khan Academy

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Explore rowspace and left nullspace concepts in matrix transformations, enhancing your understanding of multi-dimensional mathematical reasoning in linear algebra.
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1 Lesons
23 minutes
On-Demand
Free-Video
Khan Academy

Determinant and Area of a Parallelogram - Matrix Transformations - Linear Algebra - Khan Academy

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Explore the relationship between 2x2 matrix determinants and parallelogram areas in linear algebra, enhancing understanding of matrix transformations and geometric interpretations.
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1 Lesons
22 minutes
On-Demand
Free-Video
Khan Academy

Showing That Inverses Are Linear - Matrix Transformations - Linear Algebra

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Explore the linearity of inverse transformations in matrix algebra, enhancing your understanding of linear algebra concepts and their applications in multidimensional reasoning.
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1 Lesons
21 minutes
On-Demand
Free-Video
International Mathematical Union

Marie-France Vignéras- Modular Representations of P-Adic Groups

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Explore modular representations of p-adic groups in the Langlands program, examining their connections to number theory and geometry using various vector spaces and modules.
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1 Lesons
56 minutes
On-Demand
Free-Video
ICTP Mathematics

Differential Geometry - Lecture 1

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Explore fundamental concepts and principles of differential geometry in this comprehensive lecture by mathematician Claudio Arezzo.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
Fields Institute

The Non-Commutative Analytic Toeplitz Algebra and Free Semigroup Algebras

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Explore non-commutative analytic Toeplitz algebra and free semigroup algebras, covering topics like weak operator topology, functional calculus, and invariant subspaces.
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19 Lesons
54 minutes
On-Demand
Free-Video
NIOS

Advanced Engineering Mathematics

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Comprehensive exploration of advanced mathematical concepts, including complex analysis, transforms, probability, linear algebra, and more, with applications to engineering problems.
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36 Lesons
1 day 10 hours
On-Demand
Free-Video
Tom Rocks Maths

Oxford Linear Algebra - Linear Transformations Explained

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Explore linear transformations with Oxford mathematician Dr Tom Crawford, covering definitions, properties, and examples in R3, including matrix multiplication and differentiation.
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1 Lesons
33 minutes
On-Demand
Free-Video
Tom Rocks Maths

Oxford Linear Algebra - Dimension Formula for Vector Spaces

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Explore the dimension formula for vector spaces through worked examples and a complete proof. Learn to calculate dimensions of subspaces and their intersections in R^4.
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1 Lesons
43 minutes
On-Demand
Free-Video
Tom Rocks Maths

Oxford Linear Algebra - Basis, Spanning and Linear Independence

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Explore key concepts in linear algebra: basis, spanning, and linear independence. Learn through intuitive examples and formal definitions, with worked problems in vector spaces and Cartesian planes.
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1 Lesons
42 minutes
On-Demand
Free-Video
Tom Rocks Maths

Oxford Linear Algebra - Subspace Test

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Comprehensive explanation of subspace test in vector spaces, including definition, examples, and applications. Includes worked problems and links to additional resources for practice.
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1 Lesons
36 minutes
On-Demand
Free-Video
Tom Rocks Maths

Oxford Linear Algebra - What is a Vector Space?

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Explore vector space axioms with concrete examples, including addition and scalar multiplication maps, 8 key axioms, and proofs for 3D coordinate vectors. Gain insights into unique properties of vector spaces.
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1 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

The Circle and Projective Homogeneous Coordinates - Universal Hyperbolic Geometry Lecture 7a

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Introduction to projective geometry and its relation to universal hyperbolic geometry, exploring concepts like affine spaces, perspective, and one-dimensional projective geometry.
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1 Lesons
38 minutes
On-Demand
Free-Video
Insights into Mathematics

Applications of 2x2 Matrices - Wild Linear Algebra A6

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Explores 2x2 matrices, focusing on coordinate changes, linear equations, vector operations, and determinants. Covers fundamental concepts and applications in linear algebra.
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27 Lesons
44 minutes
On-Demand
Free-Video
Insights into Mathematics

Projective View of Conics and Quadrics - Differential Geometry Lecture 9

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Explore projective geometry's application to conics and quadrics, using homogeneous coordinates to unify the study of algebraic curves and surfaces in plane and space.
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1 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

Integral Row Reduction and Hermite Normal Form - Math Foundations 223

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Explores integral row reduction algorithm for finding a basis of integral linear space, paralleling Euclid's algorithm. Introduces Hermite normal form for msets of vexels in abstract algebra context.
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1 Lesons
44 minutes
On-Demand
Free-Video
Insights into Mathematics

Lattice Relations and Hermite Normal Form - Abstract Algebra Math Foundations 224

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Explore lattices and integral linear spans of vexels, including the Hermite normal form algorithm for understanding lattice structure and relations between elements in a spanning set.
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1 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Linear Spaces and Spans II - MathFoundations 220

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Introduction to integral linear spaces as abstract algebraic objects, exploring their applications in mathematics, chemistry, and physics. Foundational concepts for linear algebra using vexel language for concrete examples.
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1 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Linear Spaces and Spans I - Abstract Algebra Math Foundations 219

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Introduction to linear spaces and spans, generalizing natural numbers with addition to form spans of multisets. Explores fundamental concepts in abstract algebra and linear algebra.
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1 Lesons
24 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Snake Lemma and Indecomposable Chain Maps

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Explore the snake lemma's connecting homomorphism through vector space chain complexes, using Escolar and Hiraoka's representation to simplify proofs and reveal key indecomposable chain maps.
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1 Lesons
45 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Linear Algebra - Lecture 2

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Explore fundamental concepts of linear algebra, including vector spaces, linear transformations, and matrix operations, essential for understanding data assimilation techniques in atmospheric sciences.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Finite Dimensional Vector Spaces - An Overview

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Comprehensive overview of finite dimensional vector spaces, exploring key concepts, properties, and applications in linear algebra and mathematical analysis.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Linear Algebra - Part I

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Explore fundamental concepts of linear algebra, including vector spaces, matrices, and linear transformations, laying the groundwork for advanced mathematical applications.
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1 Lesons
1 hour 38 minutes
On-Demand
Free-Video
Wrath of Math

Orthogonal Matrices and Their Properties - Linear Algebra

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Explore orthogonal matrices: definition, examples, properties, and geometric interpretations. Learn about their equivalence to matrices with orthonormal row and column vectors.
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7 Lesons
17 minutes
On-Demand
Free-Video
Wrath of Math

Gram-Schmidt Orthogonalization - Proof and Example in Linear Algebra

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Comprehensive exploration of Gram-Schmidt orthogonalization, covering proof, process, and practical application in R^3. Ideal for deepening understanding of orthonormal bases in linear algebra.
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6 Lesons
15 minutes
On-Demand
Free-Video
Wrath of Math

The Four Fundamental Subspaces and the Fundamental Theorem of Linear Algebra

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Explore fundamental subspaces in linear algebra: row, column, null, and left null spaces. Learn their relationships, dimensions, and orthogonality, culminating in the fundamental theorem.
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8 Lesons
22 minutes
On-Demand
Free-Video
Wrath of Math

Least Squares Solutions and Deriving the Normal Equation - Linear Algebra

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Explore least squares solutions, deriving the normal equation for inconsistent systems. Learn best approximation theorem, its application in R^n, and solve examples with unique and infinite solutions.
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12 Lesons
25 minutes
On-Demand
Free-Video
Wrath of Math

Matrices for General Linear Transformations - Linear Algebra

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Explore transformation matrices for linear transformations, including coordinate translation, matrix multiplication, and formula derivation. Gain practical insights through examples and applications in linear algebra.
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8 Lesons
18 minutes
On-Demand
Free-Video
Wrath of Math

Isomorphic Vector Spaces and Isomorphisms - Linear Algebra

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Explore isomorphic vector spaces and their properties, including examples and proofs. Learn how all n-dimensional spaces relate to R^n and understand key concepts in linear algebra.
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17 Lesons
17 minutes
On-Demand
Free-Video
Wrath of Math

Composition of Linear Transformations - Linear Algebra

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Explore composition of linear transformations, including definitions, proofs, examples, and theorems. Learn about order, multiple compositions, and one-to-one transformations in linear algebra.
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10 Lesons
17 minutes
On-Demand
Free-Video
Wrath of Math

Inverse Linear Transformations - Definition and Properties

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Explore inverse linear transformations: definition, properties, and examples. Learn how to prove their one-to-one nature and find inverses in this concise, informative video on advanced linear algebra concepts.
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6 Lesons
14 minutes
On-Demand
Free-Video
Wrath of Math

One-to-One and Onto Linear Transformations in Linear Algebra

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Explore one-to-one and onto linear transformations, their properties, and examples. Learn about the equivalence between these concepts and their importance in linear algebra.
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11 Lesons
16 minutes
On-Demand
Free-Video
Wrath of Math

Kernel and Range of Linear Transformations in Linear Algebra

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Explore kernel and range in linear transformations, their definitions, examples, and proof of subspace properties. Gain insights into null space and column space extensions.
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9 Lesons
14 minutes
On-Demand
Free-Video
Wrath of Math

General Linear Transformations on Vector Spaces

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Explore general linear transformations on vector spaces, their properties, and examples. Learn to distinguish between linear and non-linear transformations in this comprehensive overview.
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13 Lesons
17 minutes
On-Demand
Free-Video
Wrath of Math

Quadratic Forms in Matrix Notation - Linear Algebra

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Explore quadratic forms in matrix notation for R^2 and R^3, learning how to write and interpret these essential linear algebra concepts with clear examples and explanations.
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1 Lesons
14 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Rank of a Matrix - Lecture 6.2

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Explore the concept of matrix rank, its properties, and applications in linear algebra. Learn methods for determining rank and its significance in solving systems of equations.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Basics of Linear Algebra - Linear Independence

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Explore linear independence, vector spaces, and basis concepts in linear algebra. Gain foundational knowledge for advanced mathematical applications.
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1 Lesons
38 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Invariant Subspaces, Eigenvalues, and Eigenvectors

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Explore invariant subspaces, eigenvalues, and eigenvectors to deepen your understanding of linear algebra concepts and their applications.
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1 Lesons
34 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Column Space, Null Space, and Rank of a Matrix

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Explore key concepts of linear algebra: column space, null space, and matrix rank. Learn general methods and practical applications through examples.
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6 Lesons
25 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Sums, Direct Sums and Gaussian Elimination

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Learn about sums, direct sums, and Gaussian elimination in linear algebra. Explore fundamental concepts and techniques for solving systems of linear equations efficiently.
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1 Lesons
45 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Vector Spaces: Introduction

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Explore fundamental concepts of vector spaces, laying the groundwork for advanced linear algebra and mathematical analysis.
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1 Lesons
25 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Properties of Eigenvalues

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Explore key properties of eigenvalues in linear algebra, enhancing understanding of matrix transformations and their applications in various fields.
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1 Lesons
12 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Linear Combinations and Span - Introduction to Vector Spaces

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Explore linear combinations and span concepts through intuitive explanations and graphical illustrations. Master fundamental linear algebra principles.
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6 Lesons
17 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Trace Theory: Trace Map and Its Range - Part 1

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Explore trace theory fundamentals, focusing on trace maps and their ranges in this concise introduction to the mathematical concept.
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1 Lesons
18 minutes
On-Demand
Free-Video
HyperComplex Seminar

Full Set of Invariants Characterizing Sp(n)-Orbits in Real Grassmannians GR(k, 4n)

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Explore invariants characterizing Sp(n)-orbits in real Grassmannians GR(k, 4n), focusing on Hermitian quaternionic structures, isoclinic subspaces, and canonical I-decomposition.
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1 Lesons
49 minutes
On-Demand
Free-Video
HyperComplex Seminar

Monogenic Functions in Infinite-Dimensional Vector Spaces with Commutative Multiplication and Harmonic Vectors

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Explore monogenic functions in infinite-dimensional vector spaces, their relation to spatial harmonic functions, and implications for complex analysis beyond traditional Cauchy integral formulas.
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1 Lesons
49 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Basis and Dimension

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Explore fundamental concepts of linear algebra, focusing on basis and dimension in vector spaces. Gain insights into key mathematical principles and their applications.
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1 Lesons
46 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Basis - Lecture 2.2

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Explore the fundamental concept of basis in linear algebra, enhancing your understanding of vector spaces and linear transformations.
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1 Lesons
39 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Linear Independence - Lecture 2.1

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Explore the concept of linear independence in vector spaces, understanding its significance and applications in linear algebra.
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1 Lesons
39 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Dimension - Lecture 2.3

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Explore the concept of dimension in mathematics, understanding its fundamental principles and applications in various fields.
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1 Lesons
40 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Manifolds, Coordinates and Tensors - Lecture 5

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Explore manifolds, coordinates, and tensors in this graduate-level physics lecture, covering key concepts and transformations for advanced theoretical understanding.
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5 Lesons
1 hour 48 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Affine and Euclidean Geometry - The Modern Approach

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Explore modern approaches to affine and Euclidean geometry, with applications to electrodynamics and relativity theory in this advanced physics lecture.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Finite Point Configurations in Euclidean, Discrete, and Arithmetic Settings

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Explore finite point configurations across Euclidean, discrete, and arithmetic spaces. Discover size requirements for subsets containing congruent copies of given configurations, with connections to learning theory.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
ICTP Mathematics

Invariants of Manifolds From 6 Dimensions

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Explore invariants of 6-dimensional manifolds, covering vector spaces, complex numbers, and vertex operator algebras. Delve into state field correspondence and multi-dimensional environments.
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11 Lesons
1 hour 1 minute
On-Demand
Free-Video
Discover AI

The Art of Text to Vector Transformation - A Comprehensive Look at AI and NLP Transformers

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Dive into the fundamentals of converting text to mathematical vectors, understanding tokenization methods like BERT and BPE for NLP applications and AI transformer models.
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1 Lesons
13 minutes
On-Demand
Free-Video
Institute for Advanced Study

Tropical Quiver Representations and Their Geometric Applications

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Delve into advanced algebraic geometry concepts through tropical quiver representations, exploring Grassmannians, flag varieties, and their matroidal analogues as fundamental moduli spaces.
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1 Lesons
58 minutes
On-Demand
Free-Video
UofU Data Science

Dimensionality Reduction: Data Matrices and Projection Methods - Lecture 18

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Explore dimensionality reduction techniques through matrix operations, focusing on dot product projections and orthogonal basis sets for effective data transformation.
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1 Lesons
51 minutes
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Free-Video
Simons Institute

A Quasi-Monte Carlo Algorithm for Smooth Kernel Evaluation

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Explore a novel data structure for density queries, combining discrepancy theory and LSH to build sparse coresets and enhance smooth kernel evaluation algorithms.
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1 Lesons
42 minutes
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Applied Algebraic Topology Network

Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules

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Efficient algorithm for computing generalized ranks of persistence modules using unfolding to zigzag modules, with applications in algebraic topology and data analysis.
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1 Lesons
46 minutes
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UofU Data Science

Singular Value Decomposition and Rank-K Approximation - Lecture 19

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Dive into Singular Value Decomposition (SVD) concepts, exploring vector path tracing and rank-k approximation techniques for advanced matrix analysis and dimensionality reduction.
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1 Lesons
1 hour 24 minutes
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Discover AI

A Brief History of AI and AI Agents - From Language Models to Multi-Agent Systems

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Explore the evolution of AI from GPT-3 to modern multi-agent systems, covering key developments in language models, function calling, AI agents, and future implications for global artificial intelligence.
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18 Lesons
51 minutes
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Free-Video