Lectures related to Matrix Diagonalization: Spectral Theorem

Spectral Theorem Recap

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

Symmetric Matrices: Properties and Decomposition

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

Singular Value Decomposition: Applications and Interpretation

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

Diagonalization of Linear Transformations

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Subspaces, Spectra, and Projections

Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.

Symmetric Matrices: Eigenvalues and Eigenvectors

Explores the diagonalization of symmetric matrices using eigenvectors and eigenvalues, emphasizing orthogonality and real eigenvalues.

Diagonalization of Symmetric Matrices

Covers the diagonalization of symmetric matrices and the spectral theorem.

Linear Algebra: Singular Value Decomposition

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