by Shmuel Friedland and Mohsen Aliabadi
2018 / xvi + 285 pages / softcover / ISBN 978-1-611975-13-0 / List Price $69.00 / SIAM Member Price $48.30 / Order Code: OT156
Keywords: matrices, linear, linear operator, Jordan canonical form, inner product space, tensor product.
This introductory textbook grew out of several courses in linear algebra given over more than a decade and includes such helpful material as
- constructive discussions about the motivation of fundamental concepts,
- many worked-out problems in each chapter, and
- topics rarely covered in typical linear algebra textbooks.
The authors use abstract notions and arguments to give the complete proof of the Jordan canonical form and, more generally, the rational canonical form of square matrices over fields. They also provide the notion of tensor products of vector spaces and linear transformations. Matrices are treated in depth, with coverage of the stability of matrix iterations, the eigenvalue properties of linear transformations in inner product spaces, singular value decomposition, and min-max characterizations of Hermitian matrices and nonnegative irreducible matrices. The authors show the many topics and tools encompassed by modern linear algebra to emphasize its relationship to other areas of mathematics.
The text is intended for advanced undergraduate students. Beginning graduate students seeking an introduction to the subject will also find it of interest.
About the Authors
Shmuel Friedland has been Professor at the University of Illinois at Chicago since 1985. He was a visiting Professor at the University of Wisconsin, Madison; IMA, Minneapolis; IHES, Bures-sur-Yvette; IIT, Haifa; and Berlin Mathematical School. He has contributed to the fields of one complex variable, matrix and operator theory, numerical linear algebra, combinatorics, ergodic theory and dynamical systems, mathematical physics, mathematical biology, algebraic geometry, functional analysis, group theory, quantum theory, topological groups, and Lie groups. He has authored and coauthored approximately 200 papers, and in 1978 he proved a conjecture of Erdős and Rényi on the permanent of doubly stochastic matrices. In 1993 he received the first Hans Schneider prize in Linear Algebra jointly with M. Fiedler and I. Gohberg, and in 2010 he was awarded a smoked salmon for solving the set-theoretic version of the salmon problem. Professor Friedland serves on the editorial boards of Electronic Journal of Linear Algebra and Linear Algebra and Its Applications, and from 1992 to 1997 he served on the editorial board of Random and Computational Dynamics. He is the author of Matrices: Algebra, Analysis and Applications (World Scientific, 2015).
Mohsen Aliabadi received his M.Sc. in Pure Mathematics from the Department of Mathematical Science, Sharif University of Technology, Tehran, in 2012. Currently, he is a Ph.D. student under the supervision of Professor Shmuel Friedland and is a teaching assistant in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago. His interests include combinatorial optimization, matrix and operator theory, graph theory, and field theory. He has authored six papers.
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