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.
Table of Contents
Linear Algebra. Combinatorial Matrix Theory and Graphs. Numerical Methods. Linear Algebra in Other Disciplines. Computational Software. Index.
Leslie Hogben is the Dio Lewis Holl Chair in Applied Mathematics and Professor of Mathematics at Iowa State University (ISU), and the Associate Director for Diversity of the American Institute of Mathematics. She received her B.A. from Swarthmore College in 1974 and her Ph. D. in 1978 from Yale University under the direction of Nathan Jacobson. Although originally working in nonassociative algebras, in the mid-1990s, she changed her focus to linear algebra.
Dr. Hogben is the author of more than 60 research papers and particularly enjoys introducing students to mathematical research. She has or is advising three postdoctoral associates, 11 doctoral students, 12 master's students, and 30 undergraduate researchers. She is the co-director of the NSF-sponsored ISU Math REU and developed an early graduate research course for mathematics and applied mathematics graduate students at ISU.
Dr. Hogben is a frequent co-organizer of meetings, workshops, and special sessions/mini-symposia. She is the Secretary/Treasurer of the International Linear Algebra Society and an associate editor of the journals Linear Algebra and its Applications and Electronic Journal of Linear Algebra.
"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 http://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."