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

Advanced Linear Algebra -- Fall 2013

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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: