Lectures related to Orthogonal Matrices: Properties and Applications

Linear Algebra: Singular Value Decomposition

Delves into singular value decomposition and its applications in linear algebra.

Symmetric Matrices and Orthogonal Matrices

Covers the properties of symmetric matrices, orthogonal matrices, and eigenvalues.

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

Symmetric Matrices and Eigenvectors

Covers the concept of symmetric matrices, orthogonal bases, and eigenvectors.

Principal Axes Theorem

Explains the Principal Axes Theorem for symmetric matrices and quadratic forms, showing the existence of orthogonal matrices for diagonalization.

Quadratic Forms in IR³

Explores quadratic forms in IR³, matrix properties, diagonalization, and positive definite matrices.

Symmetric Matrices and Quadratic Forms

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