Lectures related to Matrix Representations of Linear Applications

Linear Algebra: Matrix Representation

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Matrix Calculus: Rank and Decomposition

Covers matrix rank, determinant, and decomposition in linear algebra.

Vector Spaces: Structure and Bases

Covers vector spaces, bases, and decomposition of vectors in R³.

Linear Algebra Review

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Matrix Representations of Linear Applications

Explores matrix representations of linear applications, including change of basis and invariants.

Matrix Representations: Linear Maps

Explores matrix representations of linear maps and their invariance, using examples and special cases.

Linear Algebra: Matrix Decomposition and Base Change

Covers the algorithm for matrix decomposition and base change in linear algebra.

Matrix Representations of Linear Applications

Covers the matrix representations of linear applications and how to find representative matrices.

Linear Applications Overview

Explores linear applications, vector spaces, kernels, and invertibility in linear algebra.

Geometric Transformations in R2 and R3

Explores geometric transformations in R2 and R3, including linear transformations, projections, matrices, and trace properties.

Matrix Representations of Linear Applications

Covers the matrix representations of linear applications and the equivalence between matrices.

Orthogonal Families and Projections

Explains orthogonal families, bases, and projections in vector spaces.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Factorisation QR: Gram-Schmidt Process

Covers the Factorisation QR theorem and the Gram-Schmidt method for orthonormal bases.

Linear Algebra: Compositions of Applications

Explores compositions of applications and injectivity conditions in linear algebra, including restriction of applications and combinatorial proof of injections.

Integration of Rational Functions

Covers the integration of rational functions and the decomposition into irreducible factors.

Singular Value Decomposition

Covers the Singular Value Decomposition (SVD) of a matrix and its applications.

Matrix Operations: Definitions and Properties

Covers the definitions and properties of matrices, including matrix operations and determinants.

Matrix Determinants: Properties and Calculations

Covers the properties and calculations of matrix determinants, including special cases and examples.