Lectures related to Symmetric Matrices: Diagonalization

Symmetric Matrices: Properties and Decomposition

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Matrix Operations: Rules and Applications

Covers matrix operations, including multiplication, transposition, powers, and inverses, and explains how to determine if a matrix is invertible.

Linear Algebra: Matrices and Operations

Introduces key concepts in linear algebra, including matrices, operations, and numerical invariants.

Diagonalization: Eigenvectors and Eigenvalues

Covers the diagonalization of matrices using eigenvectors and eigenvalues.

Spectral Decomposition of Symmetric Matrices

Explores the spectral decomposition of symmetric matrices, including diagonalization and orthogonal basis change matrices.

Matrix Equations: Finding Free Variables

Explains how to find free variables in matrix equations and analyze characteristic polynomials.

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.