Lectures related to Matrix Computations: Complexity and Solvers

Explores least squares in linear regression, hypothesis testing, outliers, and model assumptions.

Explores operations with triangular matrices and their role in solving linear systems.

Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

Covers the Moore-Penrose pseudoinverse and its properties for arbitrary matrices.

Covers LU factorization, determinants, subspaces, and matrix products.

Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.

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

Covers the basics of linear regression and how to solve estimation problems using least squares and matrix notation.

Explores matrix inversion, conditions for invertibility, uniqueness of the inverse, and elementary matrices for inversion.