Hardcover ISBN:  9780821894910 
Product Code:  GSM/147 
List Price:  $99.00 
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AMS Member Price:  $79.20 
eBook ISBN:  9781470409456 
Product Code:  GSM/147.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821894910 
eBook: ISBN:  9781470409456 
Product Code:  GSM/147.B 
List Price:  $184.00$141.50 
MAA Member Price:  $165.60$127.35 
AMS Member Price:  $147.20$113.20 
Hardcover ISBN:  9780821894910 
Product Code:  GSM/147 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470409456 
Product Code:  GSM/147.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821894910 
eBook ISBN:  9781470409456 
Product Code:  GSM/147.B 
List Price:  $184.00$141.50 
MAA Member Price:  $165.60$127.35 
AMS Member Price:  $147.20$113.20 

Book DetailsGraduate Studies in MathematicsVolume: 147; 2013; 264 ppMSC: Primary 15; 05; 47;
Matrix theory is a classical topic of algebra that had originated, in its current form, in the middle of the 19th century. It is remarkable that for more than 150 years it continues to be an active area of research full of new discoveries and new applications.
This book presents modern perspectives of matrix theory at the level accessible to graduate students. It differs from other books on the subject in several aspects. First, the book treats certain topics that are not found in the standard textbooks, such as completion of partial matrices, sign patterns, applications of matrices in combinatorics, number theory, algebra, geometry, and polynomials. There is an appendix of unsolved problems with their history and current state. Second, there is some new material within traditional topics such as Hopf's eigenvalue bound for positive matrices with a proof, a proof of Horn's theorem on the converse of Weyl's theorem, a proof of CamionHoffman's theorem on the converse of the diagonal dominance theorem, and Audenaert's elegant proof of a norm inequality for commutators. Third, by using powerful tools such as the compound matrix and Gröbner bases of an ideal, much more concise and illuminating proofs are given for some previously known results. This makes it easier for the reader to gain basic knowledge in matrix theory and to learn about recent developments.ReadershipGraduate students, research mathematicians, and engineers interested in matrix theory.

Table of Contents

Chapters

Chapter 1. Preliminaries

Chapter 2. Tensor products and compound matrices

Chapter 3. Hermitian matrices and majorization

Chapter 4. Singular values and unitarily invariant norms

Chapter 5. Perturbation of matrices

Chapter 6. Nonnegative matrices

Chapter 7. Completion of partial matrices

Chapter 8. Sign patterns

Chapter 9. Miscellaneous topics

Chapter 10. Applications of matrices

Unsolved problems


Additional Material

Reviews

[I]n an orbit of some 250 pages or so [Zhan] travels from where a good undergraduate course (even in today's model) leaves off ... and then hits a host of rather marvelous themes including the inner life of Hermitian matrices and matrix perturbation theory, as well as some pretty exotic material such as the FrobeniusKönig Theorem and PerronFrobenius theory. ... There are plenty of exercises to be had, and the author's goal is clearly to guide able and willing graduate students toward research in this area, which certainly possesses the attractive qualities of being both accessible ... and exciting  it's algebra after all! I think Zhan will be successful in this enterprise: it's a very nice book indeed.
Michael Berg, MAA Reviews


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Matrix theory is a classical topic of algebra that had originated, in its current form, in the middle of the 19th century. It is remarkable that for more than 150 years it continues to be an active area of research full of new discoveries and new applications.
This book presents modern perspectives of matrix theory at the level accessible to graduate students. It differs from other books on the subject in several aspects. First, the book treats certain topics that are not found in the standard textbooks, such as completion of partial matrices, sign patterns, applications of matrices in combinatorics, number theory, algebra, geometry, and polynomials. There is an appendix of unsolved problems with their history and current state. Second, there is some new material within traditional topics such as Hopf's eigenvalue bound for positive matrices with a proof, a proof of Horn's theorem on the converse of Weyl's theorem, a proof of CamionHoffman's theorem on the converse of the diagonal dominance theorem, and Audenaert's elegant proof of a norm inequality for commutators. Third, by using powerful tools such as the compound matrix and Gröbner bases of an ideal, much more concise and illuminating proofs are given for some previously known results. This makes it easier for the reader to gain basic knowledge in matrix theory and to learn about recent developments.
Graduate students, research mathematicians, and engineers interested in matrix theory.

Chapters

Chapter 1. Preliminaries

Chapter 2. Tensor products and compound matrices

Chapter 3. Hermitian matrices and majorization

Chapter 4. Singular values and unitarily invariant norms

Chapter 5. Perturbation of matrices

Chapter 6. Nonnegative matrices

Chapter 7. Completion of partial matrices

Chapter 8. Sign patterns

Chapter 9. Miscellaneous topics

Chapter 10. Applications of matrices

Unsolved problems

[I]n an orbit of some 250 pages or so [Zhan] travels from where a good undergraduate course (even in today's model) leaves off ... and then hits a host of rather marvelous themes including the inner life of Hermitian matrices and matrix perturbation theory, as well as some pretty exotic material such as the FrobeniusKönig Theorem and PerronFrobenius theory. ... There are plenty of exercises to be had, and the author's goal is clearly to guide able and willing graduate students toward research in this area, which certainly possesses the attractive qualities of being both accessible ... and exciting  it's algebra after all! I think Zhan will be successful in this enterprise: it's a very nice book indeed.
Michael Berg, MAA Reviews