Lectures related to Linear Applications: Bases and Dual Spaces

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

Covers linear dependence, independence, and applications in vector spaces.

Discusses distributions, the Laplace transform, and their applications in mathematical analysis.

Introduces vector spaces, subspaces, linear maps, and evaluation maps, with examples and exercises for better comprehension.

Covers general elliptic equations, including Dirichlet problems and boundary conditions.

Covers the basics of linear mapping and coordinate systems.

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Explores basis change in linear algebra and the role of matrices.

Explores smooth manifolds through diffeomorphisms and embedded submanifolds in a linear space.