Preface to the Second Edition: Both the format and guiding vision of Handbook of Linear Algebra remain unchanged, but a substantial amount of new material has been included in the second edition. The length has increased from 1400 pages to 1900 pages. There are 20 new chapters. Subjects such as Schur complements, special types of matrices, generalized inverses, matrices over nite elds, and invariant subspaces are now treated in separate chapters. There are additional chapters on applications of linear algebra, for example, to epidemiology. There is a new chapter on using the free open source computer mathematics system Sage for linear algebra, which also provides a general introduction to Sage. Additional surveys of currently active research topics such as tournaments are also included. Many of the existing articles have been revised and updated, in some cases adding a substantial amount of new material. For example, the chapters on sign pattern matrices and on applications to geometry have additional sections. As was true in the rst edition, the topics range from the most basic linear algebra to advanced topics including background for active research areas. In this edition, many of the chapters on advanced topics now include Conjectures and Open Problems, either as a part of some sections or as a new section at the end of the chapter. The conjectures and questions listed in such sections have been in the literature for more than ve years at the time of writing, and often a number of partial results have been obtained. In most cases, the current (at the time of writing) state of research related to the question is summarized as facts. Of course, there is no guarantee that (years after the writing date) such problems have not been solved (in fact, we hope they have)-- Provided by publisher.