Applied Linear Algebra

MATH5112/6012, Fall semester, 2020

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall.

Teaching mode

Textbook

Course Description

We shall cover the following topics from core basic linear algebra (chapter numbers from the textbook),
  1. Matrices, vectors, Gaussian Elimination, matrix factorizations, Forward and Back Substitution, inverses, determinants: 1.1–1.6, 1.8–1.9.
  2. Vector spaces, subspaces, linear independence, bases, dimension: 2.1–2.5.
  3. Inner products and their associated norms: 3.1–3.3.
  4. Orthogonal vectors, bases, matrices, and projections: 4.1–4.4.
  5. Positive definite matrices and minimization of quadratic functions: 3.4–3.5, 5.2
and the following applications,
  1. Minimization, least squares, data fitting and interpolation: 4.5, 5.3–5.5.
  2. Signal processing: 3.6, 5.6.

Homework/Exams/Grades

There will be weekly homework sets, two midterm exams and a final exam. There will be optional projects on applications, for extra bonus, that would require programming skills (at your choice of programming languages: Python, R, MATLAB). The total points a student could obtain is 110 = 100 + 10 (bonus) as explained below. The letter grades will be A (90+), A- (85+), B+ (80+), B (75+), etc.

Tentative Schedule

All homework (HW) due the Monday of the next week. Optional projects (P) will be due a few weeks later as indicated. Links to be provided as semester goes.