Lectures related to Advanced Analysis II: Local Extrema and Hessians

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

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Explores diagonalization in symmetric matrices, emphasizing orthogonality and orthonormal bases.

Explores the Jacobi method and diagonalization techniques, including similarity transformation, power methods, and QR decomposition.

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.

Discusses isometries and orthonormal bases in mathematics.

Focuses on proving the uniqueness of the zero vector in the kernel of a symmetric matrix.

Explores eigenvalues, matrix trace, and similarity, highlighting their significance in matrix properties.