ECE 501B

Advanced Linear Systems Theory
Catalog Data: 

ECE 501B - Advanced linear system theory

Credits: 3.00

Course Website:

Course Assessment:

  • Homework: 6 assignments
  • Project: 1 team project
  • Exams: 2 midterm exams, 1 final exam
  • Typical grading policy: 50% midterms, 30% final exam, 10% homework, 10% project

Course Summary: Mathematical fundamentals for analysis of linear systems. Maps and operators in finite and infinite dimensional linear vector spaces, metric spaces, and inner-product spaces. Introduction to representation theory. Eigensystems. Spectral theorems and singular value decomposition. Continuity, convergence and separability. Sturm-Louisville theory.

Graduate standing or permission of the instructor


  • Axler, Sheldon. Linear Algebra Done Right. 2nd ed. Springer, 1997.
  • Franks, L.E. Signal Theory. Revised ed. Dowden & Culver, 1981. (Provided)


  • Solow, Daniel. How to Read and Do Proofs. 4th ed. Wiley, 2005.

Course Learning Outcomes: 

At the end of the course, students will be able to apply these concepts to real-world application problems in science and engineering.

Course Topics: 

  • Vector space
  • Subspace
  • Subspace sum and direct sum
  • Span and linear independence
  • Bases
  • Dimension
  • Linear maps and operators  
  • Null space and range
  • Matrix representation of a map
  • Invertability
  • Invariant subspaces (especially eigenvalues/vectors)
  • Inner products and norms
  • Orthonormal bases
  • Linear functionals and adjoints
  • Special operator forms (self-adjoint, normal, positive, isometries, etc.)
  • Real and complex spectral theorems
  • Polar and singular value decompositions
  • Trace and determinant
  • Function spaces
  • Continuity, convergence, and separabilty
  • Equivalence classes
  • Eigenfunctions

Class/Laboratory Schedule: 

One 150-minute lecture per week

Prepared by: 
Michael E. Gehm
Prepared Date: 
April 2013

University of Arizona College of Engineering