Lectures related to Linear Algebra: Orthogonal Projection and QR Factorization

Covers the theory and applications of Singular Value Decomposition in computational physics, including solving linear systems and polynomial fits.

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

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

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

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

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

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

Explores Singular Value Decomposition, matrix solutions, and least squares regression in data analysis.