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#Matrix Theory

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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
Fields Institute

Zigzag Strategy for Random Matrices

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Dive into the zigzag strategy for random matrices, exploring advanced probability concepts and their applications in matrix theory.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video

Eigenvalues

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Explore eigenvalues through diverse applications, from Zelda to Pokémon battles. Master matrix operations, differential equations, and advanced concepts like Jordan Canonical Form.
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30 Lesons
7 hours
On-Demand
Free-Video
statisticsmatt

Brief Series on Eigenvalue Inequalities

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Explore key eigenvalue inequalities for symmetric matrices, including Courant-Fischer, Weyl's, Gershgorin Circle, and Brauer's oval theorems, with applications to correlation matrices.
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6 Lesons
1 hour 30 minutes
On-Demand
Free-Video
NIOS

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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34 Lesons
1 day 8 hours
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Large Random Matrices and PDEs

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Explore connections between large random matrices and partial differential equations in this advanced mathematical lecture by Pierre-Louis Lions.
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1 Lesons
53 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

The Spectra of Some Arithmetical Matrices

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Explore the spectral analysis of GCD matrices and their connection to analytic number theory, focusing on recent developments in this classical field.
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1 Lesons
53 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Log-Sobolev Inequalities for Matrix-Valued Functions

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Explore advanced mathematical concepts of Log-Sobolev inequalities for matrix-valued functions, focusing on L1 variants and their applications in quantum systems and random matrices.
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1 Lesons
58 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Estimating Dimension and Lyapunov Exponents - Lecture 1B

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Delve into advanced mathematical concepts exploring Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems through conformal iterated function schemes.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Institute for Advanced Study

Tropicalizing Principal Minors of Positive Definite Matrices

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Delve into advanced mathematical concepts exploring tropicalization of principal minors, M-concave functions, and their relationship with tropical Grassmannian and Flag varieties.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Insights into Mathematics

Maxel Algebra I - Data Structures in Mathematics Math Foundations

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Explore maxel algebra, a new matrix theory focusing on idempotent diagonal maxels and sets of natural numbers. Learn about multiplication, identity maxels, and key propositions in this mathematical foundation.
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10 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Maxel Theory - New Thinking About Matrices II - Data Structures Math Foundations

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Exploring maxel theory as an extension of matrix theory, focusing on multiset views, distributive and associative laws, 1-maxels, and frames. Introduces new terminology and notation for a data structure-oriented approach.
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7 Lesons
27 minutes
On-Demand
Free-Video
Insights into Mathematics

Reflections and Projective Linear Algebra - Universal Hyperbolic Geometry

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Explore reflections in hyperbolic geometry through projective linear algebra. Learn about null points, reflection matrices, and the sl(2) Lie algebra. Gain insights into fundamental symmetries and their mathematical representations.
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10 Lesons
50 minutes
On-Demand
Free-Video
ICTP Mathematics

Finding Solitons in Differential Geometry

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Explore solitons in differential geometry, their role in discovering distinguished geometric structures, and applications in various mathematical contexts including Lie groups and algebras.
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11 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Tom Rocks Maths

Oxford Linear Algebra - How to Find a Matrix Inverse Using Elementary Row Operations

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Learn to calculate matrix inverses using Elementary Row Operations (ERO's) with clear explanations and worked examples for 2x2 and 4x4 matrices, including the case of non-invertible matrices.
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7 Lesons
24 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Symmetry and Determinantal Polynomials - SIAM SAGA Seminar

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Explore symmetry in determinantal polynomials, from historical roots to modern applications. Discover representations of plane curves and connections to the principal minor map in this advanced mathematics seminar.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
IEEE

Matrix Methods in Computer Science - Session 6B

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Explore advanced matrix methods and their applications in computer science, focusing on cutting-edge research and algorithmic developments.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
IEEE

Matrix Methods in Computer Science - Session 4B

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Explore advanced matrix methods and their applications in computer science, focusing on cutting-edge research and algorithmic developments.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
IEEE

Robust and Sample Optimal Algorithms for PSD Low-Rank Approximation

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Explore efficient algorithms for positive semidefinite low-rank approximation, focusing on robustness and sample optimality in matrix computations.
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1 Lesons
28 minutes
On-Demand
Free-Video
Simons Institute

Sublinear Time Eigenvalue Approximation via Random Sampling

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Explore efficient algorithms for approximating eigenvalues of large matrices using random sampling techniques, with applications in data analysis and machine learning.
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1 Lesons
47 minutes
On-Demand
Free-Video
Insights into Mathematics

Maxel Theory: New Thinking About Matrices - Math Foundations 166

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Explore Maxel theory, a novel approach to matrix theory using pixels. Learn about maxel algebra, multiplicative structure, and applications in linear algebra.
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8 Lesons
33 minutes
On-Demand
Free-Video
Insights into Mathematics

Integral Vectors and Matrices via Vexels and Maxels - Data Structures Math Foundations

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Explore integral vectors and matrices through vexels and maxels, expanding on previous concepts with a multiset framework for more flexible indexing and generalized representations.
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7 Lesons
24 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Fiber Symmetrization in the Space of Matrices

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Explore fiber symmetrization in matrix spaces, its properties, and applications to isoperimetric inequalities for convex bodies, generalizing Steiner symmetrization to higher dimensions.
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1 Lesons
27 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Minimal Rank of Submatrices of Random Rectangular Matrices

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Explore the minimal rank of square submatrices in random rectangular matrices, proving a conjecture on their behavior as matrix dimensions vary.
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1 Lesons
40 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Hypergeometric Matrix Models and their Duals

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Explore hypergeometric functions of complex matrices, their connections to algebraic combinatorics, and a novel approach to approximating these functions using Hurwitz theory concepts.
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1 Lesons
52 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

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
Institute for Mathematical Sciences

Approximately Hadamard Matrices and Random Frames

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Explore approximately Hadamard matrices and random frames with Mark Rudelson, delving into advanced mathematical concepts and their applications in signal processing and data analysis.
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1 Lesons
48 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Designing and Exploiting Fast Algorithms for Polynomial Matrices - Lecture 1

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Explorez les algorithmes rapides pour les matrices polynomiales et leurs applications en algèbre informatique dans cette conférence mathématique approfondie.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Geometry and Topology of Spaces of Structured Matrices

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Explore geometric and topological aspects of structured matrices, including momentum maps, frame spaces, and applications in compressed sensing and graph theory.
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12 Lesons
38 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

The Matrix A2 Conjecture Fails, or 3/2... - Lecture

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Explore Sergei Treil's disproof of the matrix A₂ conjecture, delving into mathematical intricacies and implications for analysis and operator theory.
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1 Lesons
43 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
Conference GSI

Determinantal Expressions of Certain Integrals on Symmetric Spaces

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Explore determinantal expressions for integrals on symmetric spaces, uncovering mathematical insights and applications in this advanced mathematical analysis.
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1 Lesons
24 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 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
Institute for Advanced Study

Total Positivity and Determinantal Inequalities

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Explore total positivity and determinantal inequalities in mathematics, focusing on advanced concepts and their applications in various fields.
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1 Lesons
23 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Positivity, Representations, and Non-Commutative Hyperbolic Geometry

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Explore total positivity in matrices, its generalization to split real Lie groups, and a new notion of positivity in flag varieties with applications to higher Teichmüller spaces.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

The Miracle of Integer Eigenvalues in Finite Poset Matrices

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Explore the fascinating connection between finite posets and integer eigenvalues in matrix theory, with implications for symmetric group representations.
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1 Lesons
30 minutes
On-Demand
Free-Video
BIMSA

Total Positivity: Combinatorics, Geometry and Representation Theory

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Explore total positivity theory in matrices, its applications, and recent developments in combinatorics, geometry, and representation theory.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

When is the Resolvent Like a Rank One Matrix? - Anne Greenbaum

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Explore when the resolvent resembles a rank one matrix in this mathematical analysis of linear algebra concepts and applications.
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1 Lesons
30 minutes
On-Demand
Free-Video
Tobias Osborne

Symmetries and Quantum Mechanics - Orthogonality Relations for Characters - Lecture 5

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Explore the fundamental principles of group representation theory in quantum mechanics, focusing on character orthogonality relations and their applications in quantum states.
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10 Lesons
1 hour 16 minutes
On-Demand
Free-Video
Kavli Institute for Theoretical Physics

Living in the Matrix - Recent Advances in Understanding Quantum Spacetime

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Explore recent advances in quantum gravity, including "random matrix" models for spacetime emergence, and their implications for understanding black holes and the universe's origins.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Coupled Oscillators: Matrices - Lecture by Supurna Sinha

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Explore coupled oscillators and matrix applications in physics. Gain insights into theoretical aspects through hands-on experiments and open-ended discussions. Designed for women pursuing physics careers.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Random Matrices and Statistical Physics - Lecture 2

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Explore connections between random matrices and statistical physics, delving into advanced mathematical concepts and their applications in complex systems analysis.
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1 Lesons
1 hour 44 minutes
On-Demand
Free-Video
TheIACR

Linear Layers in Cryptography - Session from Fast Software Encryption 2023

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Explore field structures, linear layers, and matrix decompositions in cryptography. Learn about evolutionary matrices and their applications in software encryption.
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11 Lesons
1 hour 5 minutes
On-Demand
Free-Video
IEEE

Rigid Matrices from Rectangular PCPs

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Explore rigid matrices, low rank matrices, and rectangular PCPs in this technical talk on advanced mathematical concepts and their applications.
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11 Lesons
22 minutes
On-Demand
Free-Video
Joint Mathematics Meetings

Proving Analytic Inequalities

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Explore advanced mathematical concepts with Avi Wigderson as he delves into proving analytic inequalities, covering Cauchy-Schwarz, Loomis-Whitney, and Young inequalities.
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18 Lesons
54 minutes
On-Demand
Free-Video
Squid: Schools for Quantum Information Development

Sample-Optimal Quantum Process Tomography with Non-Adaptive Incoherent Measurements

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Delve into quantum process tomography theory, exploring sample complexity bounds for learning quantum channels using non-adaptive incoherent measurements and diamond norm approximations.
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10 Lesons
27 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
On-Demand
Free-Video
BIMSA

A Geometrical Interpretation of Universally Quantified Inequalities and Its Applications to Mathematics

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Explore a geometrical interpretation of universally quantified inequalities and its applications across mathematics, focusing on Shannon entropy and connections to various mathematical branches.
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1 Lesons
37 minutes
On-Demand
Free-Video
Institute for Advanced Study

Valuated Delta Matroids and Principal Minors

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Delve into advanced mathematical concepts of valuated Delta matroids, their relationship with principal minors of Hermitian matrices, and their applications in combinatorial structures.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
UofU Data Science

Data Influence: Understanding Influence Functions and Efficiency in Machine Learning

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Delve into advanced mathematical concepts of data influence, exploring influence functions, efficiency, and convexity through theoretical frameworks and practical applications in data science.
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8 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

An Approach Towards the Aaronson-Ambainis Conjecture via Fourier Completely Bounded Polynomials - Part 1

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Delve into quantum computing theory through an analysis of the Aaronson-Ambainis conjecture, exploring its relationship with Fourier completely bounded polynomials and implications for quantum algorithm simulation.
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1 Lesons
47 minutes
On-Demand
Free-Video
Michael Penn

Understanding the Determinant Formula in Linear Algebra

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Uncover the mathematical reasoning and intuition behind determinant formulas through clear explanations and step-by-step derivations of this fundamental linear algebra concept.
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1 Lesons
18 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

New Signed Bijections Pertaining to Alternating Sign Matrices and Gelfand-Tsetlin Patterns

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Delve into discrete integrable systems through exploration of difference equations, cluster algebras, and probabilistic models, focusing on mathematical physics and combinatorial structures.
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1 Lesons
23 minutes
On-Demand
Free-Video
USENIX

Less is More: Revisiting the Gaussian Mechanism for Differential Privacy

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Explore groundbreaking improvements to differential privacy through a novel Rank-1 Singular Multivariate Gaussian mechanism that enhances data protection while minimizing accuracy loss in high-dimensional queries.
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1 Lesons
12 minutes
On-Demand
Free-Video