More Applications of 2x2 Matrices - Wild Linear Algebra A
Explores advanced applications of 2x2 matrices in linear algebra, covering rotations, reflections, composition of transformations, and connections to calculus, with a focus on linear approximations and derivatives.
Change of Coordinates and Determinants - Wild Linear Algebra A
Explore change of coordinates, linear equations, vectors, matrices, and determinants in linear algebra. Gain insights into fundamental concepts and their applications through examples and exercises.
Area and Volume - Wild Linear Algebra A | NJ Wildberger
Explore area and volume in linear algebra using bi-vectors and tri-vectors. Learn algebraic formulations, geometric proofs, and applications in physics and electromagnetism.
Center of Mass and Barycentric Coordinates - Wild Linear Algebra A
Explore vectors, forces, and motion through engaging games. Learn about center of mass, Archimedes' principle, and barycentric coordinates in this comprehensive linear algebra lecture.
Geometry with Vectors - Wild Linear Algebra A 2 - NJ Wildberger
Explore vector geometry, arithmetic, and affine combinations. Learn key theorems about parallelograms and triangles. Practice with exercises on vector properties and geometric relationships.
Introduction to Linear Algebra - Wild Linear Algebra A 1 - NJ Wildberger
Explore geometric approach to linear algebra, focusing on vectors, coordinate systems, and transformations. Learn essential concepts and problem-solving techniques in this foundational mathematics course.
Applications of Row Reduction - Gaussian Elimination I - Wild Linear Algebra A - NJ Wildberger
Explores row reduction applications in linear algebra: inverting matrices, finding eigenvalues/eigenvectors, and calculating determinants. Includes examples and exercises for practical understanding.
Linear Algebra With Polynomials - Wild Linear Algebra A
Explore polynomials in linear algebra, covering interpolation, regression, and isomorphism. Learn to apply geometric approaches to transformations and connect polynomial spaces with vector spaces.
The Geometry of a System of Linear Equations - Wild Linear Algebra A
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.
Rank and Nullity of a Linear Transformation - Wild Linear Algebra A - NJ Wildberger
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.
Change of Basis and Taylor Coefficient Vectors - Wild Linear Algebra A - NJ Wildberger
Explore change of basis, vatrices, and Taylor coefficients in linear algebra. Novel framework connects coordinate vectors to calculus applications, featuring generalized Pascal matrices.
Cubic Splines - De Casteljau Bezier Curves Using Linear Algebra
Explore de Casteljau Bezier curves and cubic splines using linear algebra, focusing on their elegant formulas and applications in design work from automobiles to modern graphics.
An Informal Introduction to Abstract Algebra
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.
The Stern-Brocot Tree, Matrices and Wedges - Real Numbers and Limits Math Foundations
Explore the Stern-Brocot tree's matrix and geometric representations, including wedges, for a deeper understanding of fractions and their relationships in mathematics.
Rational Trigonometry in Three Dimensions - Universal Hyperbolic Geometry
Extending rational trigonometry to 3D using vectors and dot products. Explores quadrance, spread, and key trigonometric laws. Introduces solid spread and determinants for three vectors.
Reflections and Projective Linear Algebra - Universal Hyperbolic Geometry
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.
Non-Euclidean Geometry - Math History - NJ Wildberger
Explore the complex history and modern interpretations of non-Euclidean geometry, challenging traditional narratives and proposing new perspectives on this fundamental mathematical concept.
Duality and Perpendicularity - Universal Hyperbolic Geometry
Explore perpendicularity in universal hyperbolic geometry, including duality, altitudes, and key theorems. Learn about unique aspects like perpendicular points and their applications in geometric analysis.
Polynomials and Sequence Spaces - Wild Linear Algebra - NJ Wildberger
Explore polynomials as sequences, introducing factorial powers and difference operators. Learn about forward/backward differences, Newton's theorem, and formulas for summing series, with practical examples and exercises.
Bases of Polynomial Spaces - Wild Linear Algebra - NJ Wildberger
Explore polynomial spaces through linear algebra, focusing on bases, translations, and derivatives. Gain insights into calculus concepts from an algebraic perspective, emphasizing practical applications and theoretical foundations.
More Row Reduction With Parameters - Wild Linear Algebra A
Explores advanced row reduction techniques with parameters, focusing on solving linear equations, vector representations, and applications in 2D and 3D spaces. Includes practical examples and exercises.