Matrix decomposition (LU, LDLt, Choleski), Numerical Solution of Linear Systems (LU, SOR, Conjugate Gradient method). Numerical Determination of Eigenvalues and Eigenvectors: iterative methods (power method and variations), Sturm sequence, Transformation methods (Jacobi, Givens, Householder, LR, QR). Linear least squares method, Singular-value decomposition (SVD), Pseudoinverse.

Laboratory exercise: Implement matlab (/Julia) code for solving numerical problems of linear algebra.