**Student Mathematical Library**

Volume: 44;
2008;
215 pp;
Softcover

MSC: Primary 15;

Print ISBN: 978-0-8218-4419-9

Product Code: STML/44

List Price: $38.00

Individual Price: $30.40

**Electronic ISBN: 978-1-4704-1218-0
Product Code: STML/44.E**

List Price: $38.00

Individual Price: $30.40

#### Supplemental Materials

# A (Terse) Introduction to Linear Algebra

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*Yitzhak Katznelson; Yonatan R. Katznelson*

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.

#### Table of Contents

# Table of Contents

## A (Terse) Introduction to Linear Algebra

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface ix10 free
- 1 Vector Spaces 112 free
- 2 Linear Operators and Matrices 3546
- 3 Duality of Vector Spaces 5768
- 4 Determinants 6576
- 5 Invariant Subspaces 8596
- 6 Inner-Product Spaces 103114
- 7 Structure Theorems 135146
- 8 Additional Topics 159170
- A Appendix 187198
- Index 211222
- Symbols 215226
- Back Cover Back Cover1230

#### Readership

Undergraduate and graduate students interested in linear algebra.

#### Reviews

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

...embodies a beautiful, concise and precise treatment of the subject as a part of general algebra. ... Students of pure mathematics will cherish this book as a wonderful, direct path through linear algebra in a general algebraic setting.

-- Zentralblatt MATH