MA3046 Matrix Analysis

This course provides students in the engineering and physical sciences curricula with an applications-oriented coverage of major topics of matrix and linear algebra. Matrix factorizations (LU, QR, Cholesky), the Singular Value Decomposition, eigenvalues and eigenvectors, the Schur form, subspace computations, structured matrices. Understanding of practical computational issues such as stability, conditioning, complexity, and the development of practical algorithms.

Prerequisite

MA2043 and EC1010

Lecture Hours

4

Lab Hours

1

Course Learning Outcomes

• How to manipulate and interpret matrix and vector norms
• The student will learn complexity analysis to understand the computational cost of the algorithms
• The student will learn floating point arithmetic and how floating point numbers are stored on computers
• The student will learn the concepts of linear algebra and use this knowledge to construct working computer code for the four projects
• Construct singular value decomposition and understand the connection to eigenvalue decomposition
• Construct orthogonalization of vectors, building QR factorizations, and to use these concepts to solve linear least-squares problems
• Construct LU factorizations, to solve systems of linear equations for square matrices for both full matrices and sparse banded matrices.
• Compute eigenvalues of diagonalizable matrices using iterative methods such as Arnoldi iteration
• Arnoldi iteration then allows the student to understand iterative methods for solving systems of linear equations using the generalized minimal residual (GMRES) method
• The role of preconditioning in accelerating the convergence of iterative matrix solvers