Description

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

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and minimum grade of C- in MATH310.

Level of Rigor

Advanced

Sample Textbooks

Linear Algebra Done Right, by Sheldon Axler

Linear Algebra by Curtis

Applications

If you like this course, you might also consider the following courses

Math403

Additional Notes

Students interested in grad school in AMSC should consider this course

Students interested in grad school in MATH should strongly consider this course

Students interested in grad school in STAT should consider this course  

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 decompositions

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