Lectures related to Orthogonal Matrices & Spectral Decomposition

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Covers the geometric description of orthogonal projections and reflections in 2D, focusing on transformations and their properties.

Explores the diagonalizability of symmetric matrices and their eigenvectors in an orthonormal basis.

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

Explores symmetric matrices, diagonalization, and quadratic forms properties.

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

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