Lectures related to Spectral Theorem Recap

Explores Sylvester's Inertia Theorem, relating eigenvalues to diagonal entries in symmetric matrices.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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

Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.

Covers the application of the Weingarten map on regular surfaces and the shape operator.

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

Explores the diagonalization of symmetric matrices and the importance of Singular Value Decomposition.