Lectures related to Linear Maps: Basis and Applications

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

Covers the basics of linear mapping and coordinate systems.

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

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

Explores forming bases, dependencies, and relationships in linear applications using invertible matrices and canonical bases.

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers linear applications, matrices, transformations, and the principle of superposition.

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Covers the matrix representations of linear applications and how to find representative matrices.

Covers the matrix representations of linear applications and the equivalence between matrices.

Explores linear algebra basics, emphasizing matrix representations of transformations and the importance of choosing appropriate bases.

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

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Covers the method to calculate the images of vectors in a given base.

Covers vector spaces, bases, and decomposition of vectors in R³.

Explores change of basis matrices in linear algebra, emphasizing the importance of understanding matrix transformations between different bases.

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Covers the concept of interesting subspaces related to matrices and the change of basis matrix.