A (Terse) Introduction to Linear Algebra

Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications. A (Terse) Introduction to Linear Algebra is a concise presentation of the core material of the subject--those elements of linear algebra that every mathematician, and everyone who uses mathematics, should know. It goes from the notion of a finite-dimensional vector space to the canonical forms of linear operators and their matrices, and covers along the way such key topics as: systems of linear equations, linear operators and matrices, determinants, duality, and the spectral theory of operators on inner-product spaces. The last chapter offers a selection of additional topics indicating directions in which the core material can be applied. The Appendix provides all the relevant background material. Written for students with some mathematical maturity and an interest in abstraction and formal reasoning, the book is self-contained and is appropriate for an advanced undergraduate course in linear algebra.

The self-contained, well-written work assumes mathematical maturity...It is a concise, thorough introduction to linear algebra. --Choice

This little book is a pleasure to read... In short, there are many who can get a substantial amount out of this little book, and I am definitely glad to have read it... --MAA Reviews

The book is written in an elegant, condensed way. It contains many exercises, mostly of theoretical character. The main advantage (in particular for teachers and talented students) is that basic ideas are carefully isolated and presented in a simple, minimal and understandable way. --European Mathematical Society Newsletter