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1 Fundamental concepts: Vector and matrix norms, linear independence, positive definite matrix
2 Direct solution methods for linear systems
(Gauss-elimination and Gauss Jordan methods, pivoting, Cramer method)
3 Direct solution methods for linear systems
(LU and Cholesky Decompositions)
4 Direct solution methods for linear systems
(QR Decomposition)
5 Iterative solution methods for linear systems and convergence analysis
(Jacobi methods)
6 Iterative solution methods for linear systems
(Gauss-Seidel method and SOR methods)
7 Solution of linear systems with up-to-date programming languages
8 Eigenvalue-eigenvector problems, Definitions, Cayley-Hamilton theorem, Diagonalizability
9 Eigenvalue-eigenvector problems, Similar matrices, Applications of diagonalizing and quadratic forms
10 Eigenvalue-eigenvector problems
(Gerschgorin disks, Rayleigh quotient)
11 Eigenvalue-eigenvector problems
(Trace method, Power and inverse power methods)
12 Eigenvalue-eigenvector problems
(Power method with shifting)
13 Solution of eigenvalue-eigenvector problems with up-to-date programming languages
14 Singular Value Decomposition (SVD) |