Lectures related to Direct Methods for Solving Linear Equations

Covers the Choleski factorisation method for solving linear systems efficiently.

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

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

Explores the conditions for LU factorization without permutation and diagonal dominance in matrices.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

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

Explores the effect of rounding errors in solving linear systems using the LU factorization method.