Teaching module
Matrix Analysis for Signal Processing with MATLAB Examples
The course provides an overview on some topics in matrix theory together with their intrinsic interaction with and application to signal processing.
Overview
The course provides an overview on some topics in matrix theory together with their intrinsic interaction with and application to signal processing. The most important and “useful” tools, methods, and matrix structures are emphasized and complemented with MATLAB examples. The lectures cover basic matrix structures and operations, the concept of matrix norm, orthonormal matrices, Householder transformations, Givens rotation, QR factorization, singular value decomposition, positive (negative) semidefinite matrices and their eigenvalue characterization, Schur complement, Cholesky factorization, matrix gradient, least square problems, Kronecker product.
Schedule topics
- Basic matrix structures and operators. MATLAB examples.
- Matrix norms. Orthonormal matrices, Matrix inverse. MATLAB examples.
- Singular Value Decomposition. Quadratic forms and positive (negative) semidefinite matrices. MATLAB examples.
- Schur complement. Cholesky factorization Eigenvalues and Eigenvectors. Matrix calculus. MATLAB examples.
- Matrix Gradient. Least Square problems. Kronecker product. MATLAB examples.
- Householder transformations. Givens rotation. QR factorization. MATLAB examples.
- Exercises and assessment test