Applied Linear Algebra

MATH5112/6012, Fall semester, 2022

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall.
Class Meeting: MWF, 1:25-2:20pm, 60 W Charlton, Room 240.
Office Hours: by appointment.

Textbook

Course Description

We shall cover the following topics from core basic linear algebra (chapter numbers from the textbook),
  1. (Review) 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. Positive definite matrices and minimization of quadratic functions: 3.4–3.5, 5.2.
  5. Orthogonal vectors, bases, matrices, and projections: 4.1–4.4.
  6. Eigenvalues and eigenvectors: 8.2–8.3.
and the following applications,
  1. Cholesky factorization for simulations of Gaussian processes.
  2. Signal processing: 3.6, 5.6.
  3. Spectral clustering (graph theory).

Homework/Exams/Grades

There will be 5 homework sets, 3 projects (including an optional one for extra bonus credit), 1 midterm exam and a final exam. The projects require some minimal programming skills (at your choice of programming languages: Python, R, MATLAB). The total points a student could obtain is 115 = 100 + 15 (bonus) as explained below. The letter grades will be A (90+), A- (85+), B+ (80+), B (75+), etc.

Tentative Schedule

Please check exact due time for homework (HW) and projects (P) at Canvas. All download/submissions via Canvas.