Linear System of Equations, Gauss Elimination, Lu and Cholesky Decomposition, Positive Definite Matrices, Least Squares And Pseudo-inverse, Weighted Least-squares, Tikhonov's Regularisation, Inner-products and Normed-vector Spaces, Orthogonality, Qr and Its Uses, Eigenvalues and Singular Values, The Svd Decomposition and Its Uses, Itrative Methods For Solving Linear and Least-squares Problems, Matrix Induced Norms, Gershgorin's Theorem, The Power Method, Numerical Instability and Numerical Erros, Toeplitz and Circulant Matrices, Convolution, The Discrete Fourier Transform and The Fft. Learning Outcomes# By The End of The Course The Studetns Will Be Able To# 1. Use Elementary Decomposition Methods in Numerical Linear Algebra - Lu, Qr, and Svd - According to Their Use and Computational Complexity. 2. Build Algorithms For The Solution of Linear Systems of Equations, Least-squares Problems, and Identification of Eigenvalues And Eigenvectors, By Choosing The Proper Solvers Based On The Properties Of The Problems and Their Dimensions._ 3. Prove Convergence of Iterative Methods For Solving Numerical Problems Via Eigen-analysis, Operators' Norms, and Gershgorin's Disk Theorem. 4. Compute The Discrete Fourier Transform On Vectors, and Diagonalize Circulant Matrices._ 5. Prove Various Advanced Theorems in Linear Algebra Regarding Eigendecomposition of Symmetric, Circulant and Positive Definite Matrices.