An Introduction to Linear Algebra

The new edition of this textbook will provide students of varied backgrounds with a comprehensive and accessible introduction to the primary subject matter of linear algebra. The contents include detailed accounts of matrices and determinants (chapters 2 to 4), finite-dimensional vector spaces (chapter 5), linear mappings (chapters 6 and 7), and (spread through chapters 2, 3, 5 and 6) the applications of these ideas to systems of linear equations, while later chapters (8 to 10) discuss eigenvalues, diagonalization of matrices, euclidean spaces, and quadratic forms. In writing the book, my constant aim has been to draw on my considerable experience of teaching this material to produce an account of it that students striving to gain an understanding of linear algebra will find helpful. In particular, therefore, I have provided suitably detailed explanations of points which students often find difficult. The reader will see that little is taken for granted. For example, the accounts of matrices and vector spaces are self-contained and start right at the begin ning. However, a basic knowledge of elementary ideas and notations con cerning sets is assumed, and from chapter 5 onwards the reader must be able to understand simple arguments about sets (such as proving that one set is a subset of another). Then, from chapter 6 onwards, a knowledge of mappings becomes essential, though to help the reader an appendix on mappings pro vides a condensed summary of everything relevant.