## About this book

### Introduction

**Basic Linear Algebra** is a text for first year students, working from concrete examples towards abstract theorems, via tutorial-type exercises. The book explains the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations, and complex numbers. Linear equations are treated via Hermite normal forms, which provides a successful and concrete explanation of the notion of linear independence. Another highlight is the connection between linear mappings and matrices, leading to the change of basis theorem which opens the door to the notion of similarity. The authors are well known algebraists with considerable experience of teaching introductory courses on linear algebra to students at St Andrews. This book is based on one previously published by Chapman and Hall, but it has been extensively updated to include further explanatory text and fully worked solutions to the exercises that all 1st year students should be able to answer.

### Keywords

Eigenvalue Eigenvector Matrix algebra equation geometry linear algebra theorem

#### Authors and affiliations

- Thomas S. Blyth
- Edmund F. Robertson

- 1.School of Mathematics and Computer ScienceUniversity of St AndrewsNorth Haugh, St AndrewsUK

### Bibliographic information