Course Weekly Lecture Plan

Week	Topic
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)