This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Advanced Linear Algebra -- Fall 2013

### From Mathematics Is A Science

**MTH 485 Advanced Linear Algebra.** A second course in linear algebra. 3 hours.

- Time and Place: as needed 516 Smith Hall.
- Instructor: Peter Saveliev (call me Peter)
- Office: Smith Hall 325
- Office Hours: WF 1:30-2:30 and MW 4:00-5:00, or by appointment
- Office Phone: x4639
- E-mail: saveliev@marshall.edu
- Prerequisites: Linear algebra
- Text:
*Advanced Linear Algebra*by Steven Roman and some online articles linked below - Goals: advanced topics necessary for tensor analysis, algebraic topology, differential geometry, and homological algebra.
- Grade Breakdown:
- homework: 100%

- Letter Grades: A: 90-100, B: 80-89, C: 70-79, D: 60-69, F: <60

See also Course policy.

## Chapters

Steven Roman, *Advanced Linear Algebra*:

- Chapter 1. Vector Spaces
- Direct Sums

- Chapter 2. Linear Transformations
- Equivalence of Matrices
- Similarity of Matrices
- Similarity of Operators
- Invariant Subspaces
- Projection Operators

- Chapter 3. The Isomorphism Theorems
- Chapter 4. Modules I: Basic Properties
- Chapter 9. Real and Complex Inner Product Spaces
- Chapter 11. Metric Vector Spaces: The Theory of Bilinear Forms
- Chapter 14. Tensor Products

See also on this site: