Lectures related to Matrix Factorization: LU Decomposition

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Explains row-echelon and reduced row-echelon matrices and their role in simplifying system resolution.

Explores the link between linear systems and optimization through elimination and LU decomposition.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

Explains the Gaussian elimination algorithm with pivoting and LU factorization for linear systems.