ECE 8007 - Matrix Theory - Spring 2020

Instructor

Richard Perry, Tolentine 435, richard.perry@villanova.edu

Course Website

http://fog.misty.com/perry/mat/

Course Description

Linear transformations and linear optimization as applied to vector spaces. Topics include solution of linear algebraic equations, linear transforms and their matrices, system decomposition (diagonalization), nondiagonalization operators and Jordan form, inner products, orthogonal projection, and pseudoinverse.

Course Grading

The course grade will be based on a set of project assignments. Course assignments are to be done individually and independently. The University policy and procedures on academic integrity and students with disabilities will be followed.

Textbook

C. N. Dorny, A Vector Space Approach to Models and Optimization, Robert E. Krieger Publishing Company, Huntington, New York, 1986.

We will be using the first 6 chapters of the text. Although this text is out of print, the first 5 chapters are available online at http://www.seas.upenn.edu/~dorny/VectorSp/vector_space.html

For Villanova students the text is available at https://www.ece.villanova.edu/perry/mat/JB/

Errata - updated 12 March 2020

Chapter Outline

  1. Introduction and Appendix 1, Matrices and Determinants

  2. System Models: Transformations on Vector Spaces

  3. Linear Differential Operators - 3.4 only, pages 128.5-133.5, State Space Models

  4. Spectral Analysis of Linear Systems - 4.1-4.2, 4.3 pages 176.5-178 only, 4.4-4.5

  5. Hilbert Spaces - 5.1, 5.2 up to page 255.5

  6. Least-Square Minimization - all except pages 363-365 and 370.5-373.5

Software

For computational assistance in solving matrix problems, Octave (free), SciPy (free), or Matlab (Villanova site license) can be used.

Semester Schedule 

week#       Wed
   1   Jan.  15
   2         22
   3         29
   4   Feb.   5  A1
   5         12
   6         19  A2
   7         26
   -   Mar.   -  Spring Break
   8         11  
   9         18  A3 (3/21)
  10         25  
  11   Apr.   1  A4 (4/4)
  12          8  
  13         15  
  14         22  A5 (4/25)
  15         29  
                 A6 (5/6)