Lectures related to Linear Systems: Operations and Solutions

Explores the link between linear systems and optimization through elimination and LU decomposition.

Covers determinants, row echelon form, properties, and geometric interpretation of determinants.

Covers strategies for calculating determinants and their geometric interpretation in various dimensions.

Explores stability and solutions of linear systems in continuous and discrete time.

Covers the concept of diagonalization of matrices through the study of eigenvectors and eigenvalues.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Explores the diagonalization of matrices and the conditions for exact diagonalization, with examples demonstrating the process.

Explains matrix rank, basis, and linear independence through examples.

Covers row echelon forms and the Gauss-Jordan algorithm for solving linear systems.