Math 413 Advanced Linear Algebra
Contents
Catalog Information
Title
Advanced Linear Algebra
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
F and possibly W
Prerequisite
Math 371 recommended, but not required.
Description
Theory and advanced topics of linear algebra.
Desired Learning Outcomes
Prove: Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.
Distinguish: Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.
Construct: Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.
Categorize: Students will be able to categorize linear-algebraic structures according to their properties.
Calculate: Students will be able to calculate precisely and efficiently, choosing appropriate methods.
Prerequisites
Math 371 recommended, but not required.
Minimal learning outcomes
- Linear equations (row operations, matrix multiplication, and invertibility)
- Vector spaces
- Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)
- Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)
- Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)
- Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)
Textbooks
Possible textbooks for this course include (but are not limited to):
