Lectures related to Dynamics on Homogeneous Spaces and Interactions with Number Theory

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Explores properties and calculation tricks of determinants, including fixing rows/columns, expanding, and examples of determinant calculations.

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.