Lectures related to Smooth Manifolds: Diffeomorphisms

Explores how submanifolds can be deformed into linear patches using diffeomorphisms and the inverse function theorem.

Covers linear maps, matrices, and applications, including exercises on bases and invertibility.

Explores the properties of invertible matrices, including unique solutions and linear independence.

Covers Riemannian connections, emphasizing their properties and significance in geometry.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Offers a quick review of key linear algebra concepts essential for further topics.

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Explores linear combinations, basis determination, and vector space dimensionality through practical examples and exercises.