# ECE 501B

Fall
Catalog Data:

ECE 501B - Advanced linear system theory

Credits: 3.00

Course Website: www.ece.arizona.edu/~gehm/501

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.

Prerequisite(s):
Graduate standing or permission of the instructor
Textbook(s):

Required:

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

Suggested:

• 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
• 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