Advanced Linear Systems
Advanced level study of linear systems and associated mathematical theory including linear equations, spectral theory, normal matrices, projections, quadratic forms, discrete and continuous time dynamical systems.
Course information
New Mexico State University EE555 Advanced Linear Systems (3 credits).
Prerequisite
M480 Vector Spaces and Matrix Algebra or equivalent undergraduate Linear Algebra course.
Textbooks
- Advanced Linear Systems by C. T. Mullis
- (Optional) Matrix Analysis by R. A. Horn and C. R. Johnson
- (Optional) Matrix Analysis and Applied Linear Algebra by C. D. Meyer
Course Objectives
The objective of this course is to provide students a solid foundation in linear algebra and matrix analysis—the language of Communications, Control, and Signal Processing theory. Such a foundation will greatly assist students in understanding research articles in journals such as the IEEE Transactions on Communications and IEEE Transactions on Signal Processing and also to conduct independent research. This objective is achieved through an advanced level understanding of essential algebraic, structural, and numerical properties of linear equations and systems.
Course materials
New Mexico State University EE555 Advanced Linear Systems lecture notes, homework and solutions, laboratories, and exams.
- Lecture Notes
- Homework
- Old Exams
This page is intended as a stable home for official course documents and high-level information.
- Vector spaces, norms, and inner products
- Linear operators and system representations
- Continuous- and discrete-time state-space models
- State transition matrices and solutions of linear systems
- Controllability and observability
- Stability of linear systems (Lyapunov methods)
- Eigenvalues, eigenvectors, and spectral theory
- Diagonalization and Jordan canonical form
- Singular Value Decomposition (SVD)
- Matrix norms and condition numbers
- Positive definite matrices and quadratic forms
- Applications of matrix decompositions in system analysis
- Linear system transformations and canonical forms
- Model reduction and balanced realizations
- Linear estimation and least squares methods
- Optimization in linear systems
- Numerical methods for large-scale systems
- Applications in control, signal processing, and data science