Brief Description
"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 ha"--
Learn More about the Book
With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.
New to the Second Edition
- Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets
- New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems
- More chapters on applications of linear algebra, including epidemiology and quantum error correction
- New chapter on using the free and open source software system Sage for linear algebra
- Additional sections in the chapters on sign pattern matrices and applications to geometry
- Conjectures and open problems in most chapters on advanced topics
Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.
Review Quotes
1.
Praise for the First Edition:
a valuable compendium of information on virtually all aspects of linear algebra and its applications. This is a Herculean labor of love on the editor s part, a successful effort that should be appreciated and applauded by anyone working and/or teaching in this important area of mathematics. Every library that supports mathematics and science departments should have this encyclopedic work on its shelves.
Henry Ricardo, MAA Reviews, June 2007
Without doubts, it will be of great help for everybody who needs linear algebra in his profession, or for instructors or students looking for concepts, results, or examples.
H. Mitsch, Monatshefte fur Math, 2007
This handbook covers all the major topics of linear algebra at both graduate and undergraduate level, as well as their applications and related software packages. The handbook will be without a doubt a valuable resource for anyone using linear algebra, i.e. basically for any mathematician.
EMS Newsletter"
2.
"The second edition is substantially expanded A huge amount of thought has gone into the book. Leslie Hogben has done an outstanding job to produce a book of this size in a uniform style with such a high standard of editing and typesetting. this is certainly a book to ask your library to order and maybe even to purchase yourself."
Nick Higham (University of Manchester) on his blog https: //nickhigham.wordpress.com, March 2014
Praise for the First Edition:
" a valuable compendium of information on virtually all aspects of linear algebra and its applications. This is a Herculean labor of love on the editor s part, a successful effort that should be appreciated and applauded by anyone working and/or teaching in this important area of mathematics. Every library that supports mathematics and science departments should have this encyclopedic work on its shelves."
Henry Ricardo, MAA Reviews, June 2007
"Without doubts, it will be of great help for everybody who needs linear algebra in his profession, or for instructors or students looking for concepts, results, or examples."
H. Mitsch, Monatshefte fur Math, 2007
"This handbook covers all the major topics of linear algebra at both graduate and undergraduate level, as well as their applications and related software packages. The handbook will be without a doubt a valuable resource for anyone using linear algebra, i.e. basically for any mathematician."
EMS Newsletter"
3.
"The second edition is substantially expanded A huge amount of thought has gone into the book. Leslie Hogben has done an outstanding job to produce a book of this size in a uniform style with such a high standard of editing and typesetting. this is certainly a book to ask your library to order and maybe even to purchase yourself."
Nick Higham (University of Manchester) on his blog https: //nickhigham.wordpress.com, March 2014
Praise for the First Edition:
" a valuable compendium of information on virtually all aspects of linear algebra and its applications. This is a Herculean labor of love on the editor s part, a successful effort that should be appreciated and applauded by anyone working and/or teaching in this important area of mathematics. Every library that supports mathematics and science departments should have this encyclopedic work on its shelves."
Henry Ricardo, MAA Reviews, June 2007
"Without doubts, it will be of great help for everybody who needs linear algebra in his profession, or for instructors or students looking for concepts, results, or examples."
H. Mitsch, Monatshefte fur Math, 2007
"This handbook covers all the major topics of linear algebra at both graduate and undergraduate level, as well as their applications and related software packages. The handbook will be without a doubt a valuable resource for anyone using linear algebra, i.e. basically for any mathematician."
EMS Newsletter
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