Lectures related to Linear Algebra: Best Approximation and Properties

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

Covers fundamental linear algebra concepts like vector spaces and eigenvalues.

Introduces orthogonal and symmetric matrices in linear algebra with practical examples.

Explores vector subspaces in R4, symmetric matrices, basis vectors, and canonical forms.

Covers matrix multiplication, properties, and inverses in linear algebra.

Covers the resolution of linear systems and its link to optimization problems.

Explains the Principal Axes Theorem for symmetric matrices and quadratic forms, showing the existence of orthogonal matrices for diagonalization.

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

Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.

Focuses on proving the uniqueness of the zero vector in the kernel of a symmetric matrix.

Explores orthogonal base change in linear algebra, focusing on matrices and transformations.

Covers the proof of the symmetry of a matrix through exercises involving symmetric matrices.

Explores linear applications in vector spaces, emphasizing subspaces and properties of linear maps.

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Explains the concept of inertia benchmark, focusing on main axes and diagonal elements of the inertia tensor.

Delves into singular value decomposition and its applications in linear algebra.

Covers symmetric matrices, eigenvalues, and diagonalization process for spectral theorem applications.

Discusses quadratic forms, matrix diagonalization, and their applications in optimization problems.