EE 510 – Linear Algebra for Engineering

Course description

The intent of this course is to provide the students with the working knowledge of advanced linear algebra and matrix theory. This course is foundational to other classes in communication, control, computer engineering, signal processing, and related areas. Case studies will offer experience with practical engineering problems and computer-aided design tools used in research and industry. The course content will be motivated by examples from different application domains and it will be presented in such a way to make it of interest to students with background in control and dynamical systems, communications, signal and image processing, artificial intelligence and machine learning, computer science and engineering, optimization, robotics, power systems, systems biology, and financial engineering.

Topic

Review of matrix analysis and elementary linear algebra; inner product spaces and norms; linear independence, basis, dimension, change of basis; solutions to linear equations; Gausian elimination and LU factorization; fundamental subspaces of matrices; eigenvalues and eigenvectors; determinant; power iteration method; similarity transformations and diagonalization; Jordan canonical form; normal matrices; symmetric and sign-definite matrices; quadratic forms; singular value decomposition and matrix approximations; induced matrix norms; least-squares and least-norm problems; introduction to optimization; gradient descent and Lagrangian-based methods; linear programming; introduction to linear dynamical systems and state-space methods; additional applications.

TuTh, 3:30 - 5:20pm, OHE 122; Jan 8 - Apr 25, 2019

Instructor and Teaching Assistant

• Instructor
  Mihailo Jovanovic
  Office: EEB 324
  Office hours: Monday 3:30 - 4:30pm (or by appointment)

• Teaching Assistants
  Eugenio Grippo
  Office: EEB 321
  Office hours: Wednesday 2 - 4pm
  
  Yixian Zhu
  Office: PHE 320
  Office hours: Wednesday 4 - 6pm
  
  Runzhou Zhang
  Office: EEB 526
  Office hours: Thursday 10am - noon

Text and software

• Primary text
  

  • Instructor's lecture notes
    

• Supplementary texts
  

  • Gilbert Strang
    Linear Algebra and Its Applications
    Thomson Brooks/Cole, Fourth Edition
    

  • Alan Laub
    Matrix Analysis for Scientists and Engineers
    SIAM

• Software
  Homework sets will make a use of Matlab

Grading policy

• Homework (40%)
  Midterm exam (30%)
  Final exam (30%)

• Homework policy
  

Homework is intended as a vehicle for learning, not as a test. Moderate collaboration with your classmates is encouraged. However, I urge you to invest enough time alone to understand each homework problem, and independently write the solutions that you turn in. Homework is generally handed out every other Thursday, and it is due at the beginning of the class a week later. Late homework will not be accepted. Start early!

Homework solutions should be typed or scanned using scanners or mobile scanner applications like CamScanner and uploaded on the DEN course website (photos taken by cell-phone cameras and in formats other than pdf will NOT be accepted). Programs and simulation results have to be uploaded on the DEN course website as well.

• Tentative exam schedule
  Midterm: March 28
  Final: for the date and time of the final exam please consult the USC Schedule of Classes