This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

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Description

This course contains an abstract treatment of finite dimensional vector spaces, linear transformations and their invariants.

Prerequisites

A grade of C- or better in (MATH 240 or MATH 461 or MATH 341) and MATH 310.

Topics

Review of basic Linear algebra

Abstract vector spaces
Bases and dimension
Coordinates
Subspaces
Linear transformations
Representation of transformations by matrices
Rank and nullity
Linear functionals and duality

Determinants

Definition and properties
Permutation groups
Evaluation

Decompositions

Direct sum decompositionss
Invariant subspaces
Eigenvalues and eigenvectors
Characteristic and minimal polynomial
Diagonalizable operators
Primary decompositions
Rational and Jordan canonical forms

Inner Product Spaces

Orthonormal Bases
Adjoints
Positive, unitary and normal operators
The spectral theorem