Matrix Theory
Description
The aim of this text is to present fundamental ideas, results, and techniques concisely, mainly in matrix theory with some in linear algebra. The book contains ten chapters covering various topics ranging from rank, similarity, and special matrices, to Schur complements, matrix normality, and majorization. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. Major changes in this third edition include:
- expansion of topics such as eigenvalue continuity, matrix functions, nonnegative matrices, matrix norms, and majorization
- inclusion of more than 200 examples and more than 1500 exercises
- emphasis on basic techniques and skills for partitioned matrices through which a variety of matrix results and matrix inequalities are shown
- showcase of many majorization-type inequalities for diagonal entries, eigenvalues, and singular values of matrices.
This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for advanced undergraduate or graduate students. Prerequisites include a solid background in elementary linear algebra and calculus. The text can also serve as a reference for researchers in algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other scientific areas.
From reviews of the second edition:
The author has made a valuable contribution to the textbook literature on matrix theory, and his work will be appreciated by students and teachers of the subject. . is recommended reading for all those wishing to acquaint themselves with basic matrix theory.- Vicentiu D. Radulescu, Zentralblatt MATH
In many places several different proofs are presented for a theorem. This causes the book to be very attractive and readable. This book is useful for researchers as well as graduate students working in linear algebra, operator theory, statistics, computer science, engineering, applied mathematics, economics, and other disciplines.
- Mohammad Sal Moslehian,
Mathematical Reviews
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Person
Fuzhen Zhang is Distinguished Professor of Mathematics at Nova Southeastern University in Fort Lauderdale, Florida. He earned his Ph.D. in Mathematics from University of California at Santa Barbara (UCSB). Zhang is the author of Linear Algebra: Challenging Problems for Students (Johns Hopkins University Press) and Problems in Linear Algebra and Matrix Theory (World Scientific Publishing). In addition to this present textbook, he is also the editor of The Schur Complement and Its Applications (Springer). His academic work primarily focuses on topics in matrix analysis. Outside of academia, Zhang enjoys playing beach volleyball, pickleball, and singing Chinese folk songs.
Content
Preface to the Third Edition.- Frequently Used Notation and Terminology.- Frequently Used Terms.- 1. Elementary Linear Algebra Review.- 2. Partitioned Matrices, Rank, and Eigenvalues.- 3. Matrix Polynomials and Canonical Forms.- 4. Numerical Ranges, Norms, and Special Products of Matrices.- 5. Special Types of Matrices.- 6. Unitary Matrices and Contractions.- 7. Positive Semidefinite Matrices.- 8. Hermitian Matrices.- 9. Normal Matrices.- 10. Majorization and Matrix Inequalities.- References.- Notation.- Index.