Lectures related to Sylvester's Inertia Theorem

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

Explores examples of algebraic quotients using invariance maps and discriminant.

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Explores optimal control and KKT conditions for non-linear optimization with constraints.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Covers the theory and applications of bilinear forms in various mathematical contexts.

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