Lectures related to Matrix Calculus: Rank and Decomposition

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

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

Introduces key concepts in linear algebra, including matrices, operations, and numerical invariants.

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

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

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

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

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

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

Covers the properties and calculations of matrix determinants, including special cases and examples.

Covers matrices, linear applications, vector spaces, and bijective functions.

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

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

Covers the definitions and properties of matrices, including matrix operations and determinants.

Covers linear transformations, matrices, kernels, and properties of invertible matrices.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Explores determinants in 3D space and their role in linear algebra.

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

Explains the concept of least squares solutions and their application in finding the closest solution to a system of equations.