Lectures on linear algebra

This book is a collection of 98 short and self-contained lectures on some of the most important topics in linear algebra. There are hundreds of examples, solved exercises and detailed derivations of important results. The step-by-step approach makes the book easy to understand and ideal for self-study. One of the main aims of the book is to be a time saver: proofs are never left to the reader; all the exercises are fully solved; useful concepts from previous chapters are systematically referenced; the reader is always shown how to do the tedious algebra! The topics covered by the book are divided into 12 main parts, as follows. PART 1 - The algebra of numeric arrays; PART 2 - Linear spaces; PART 3 - Matrix rank and inversion; PART 4 - Linear maps; PART 5 - Systems of linear equations; PART 6 - Special matrices and equivalence; PART 7 - Complex vectors and inner products; PART 8 - Determinants; PART 9 - Polynomials; PART 10: Eigenvalues and eigenvectors; PART 11: Matrix polynomials; PART 12: Jordan form.