This repository contains materials related to the Practical an Theoretical classes from Computational Linear Algebra course. Below is a summary of the topics covered in the program:
- Definition of real vector spaces.
- Subspaces, generating systems, and linear independence.
- Bases and dimension of a vector space.
- Linear transformations and their matrix representation.
- Kernel, image, co-kernel, and co-image of a linear transformation.
- Vector and matrix norms.
- Cauchy-Schwarz inequality and triangular inequality.
- Error and conditioning of matrices.
- Solution of linear systems through Gaussian elimination and LU factorization.
- Orthogonal matrices and QR factorization.
- Basic properties of eigenvalues and eigenvectors.
- Gerschgorin's theorem.
- Diagonalization of matrices and eigenvector bases.
- Eigenvalues of symmetric matrices and the spectral theorem.
- Numerical methods for eigenvalue calculation (power method, QR algorithm).
- Iterative methods for linear systems (Jacobi, Gauss-Seidel, SOR).
- Krylov subspace and conjugate gradient method.
- Positive definite matrices and Cholesky factorization.
- Singular value decomposition (SVD).
- Generalized inverse and Schur decomposition.
- Jordan canonical form.
- Bilinear forms and inner products.
- Least squares problems and approximation and interpolation.
This repository provides additional resources, including example codes, reading materials, and practical exercises, to complement the study of these topics.