The following covers the basics of linear algebra. It could be used as a text for UNC’s linear algebra course, Math 577. It can also be used to provide background in the linear algebra needed to analyze systems of differential equations.

Linear Algebra

This Linear Algebra text has enough material for a year-long course. The following notes would serve for an introductory semester course.

Introduction to Linear Algebra

Here are some notes on further topics in linear algebra.

Row Rank = Column Rank

Generalized eigenspace decomposition: another proof

Variant of Schur’s Inequality

Concavity of log det on P_n

Jacobi’s generalization of Cramer’s formula

The Octonions

The Euclidean algorithm and Sl(2,Z)

Orthogonal Projections onto Ranges and Null Spaces