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MTH706 : Advanced Linear Algebra

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1. Dr. Junaid Zaidi, 2. Ataullah Kalim, 3. Shahzad Faizi
1. Ph.D (Optimization of Algorithms on Networking) , 2. Ph. D ( Fluid Mechanics ), 3. M.Phil.
1. University of Birmingham, England (UK), 2. University of Essex, Colchester, UK, 3. NUCES(FAST)

Course Contents

Introduction and Overview, Introduction to Matrices, Systems of Linear Equations, Row Reduction and Echelon Forms, Null Spaces, Column Spaces and Linear Transformations, Linearly Independent Sets, Bases, Dimension of a Vector, Rank, Solution of Linear System of Equations (Jacobi Method), Solution of Linear System of Equations (Gauss–Seidel Iteration Method), Solution of Linear System of Equations (Relaxation Method), Norms of Vectors and Matrices, Matrix Norms and Distances, Error Bounds and Iterative Refinement, Eigenvalues and Eigenvectors, The Characteristic Equation, Diagonalization, Inner Product, Orthogonal and Orthonormal set, Orthogonal Decomposition, Orthogonal basis, Gram-Schmidt Process, Orthonormal basis, Least Square Solutions, Inner Product Spaces, Applications of inner product spaces, Eigen Value Problems (Power Method), Eigen Value Problems (Jacobi’s Method), QR Algorithm and Householder’s Method, Singular Value Decomposition, Fixed Points for Functions of Several Variables, Newton’s Method, Quasi-Newton Method.