Linear Algebra: Matrix Decomposition and Base Change

Related lectures (23)

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Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Explores the unique decomposition of matrices into diagonalizable and nilpotent parts, showcasing their properties and applications.

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

Covers the composition and product of matrices, including matrix multiplication.

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Explores the Jordan normal form and its applications in linear algebra, focusing on diagonalization and cyclic bases.

Covers matrix transposition, rank, and basis change in linear algebra, exploring invertibility criteria and basis relationships.

Explores Singular Value Decomposition, low-rank approximation, fundamental subspaces, and matrix norms.

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.