Lectures related to Linear systems resolution

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

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Covers matrix rank, determinant, and decomposition in linear algebra.

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

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

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

Introduces LU decomposition for efficient linear equation solving using matrix factorization.