Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics with important applications and of special mathematical interest in matrix theory not included in the previous text. These topics include the field of values, stable matrices and inertia, singular values, matrix equations and Kronecker products, Hadamard products, and matrices and functions. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. The book should be welcomed by graduate students and researchers in a variety of mathematical fields both as an advanced text and as a modern reference work.
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Editorial Reviews
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"The writing of this and the previous book Matrix Analysis by the same authors is a wonderful achievement both for the two authors and for the field of matrix theory....a landmark book." Frank Uhlig, Linear Algebra and Its Applications
"There is no doubt that this two volume work, Matrix Analysis and Topics in Matrix Analysis is an important and unique contribution to the contemporary book literature on matrix theory." Marvin Marcus, Bulletin of the American Mathematical Society
"I can recommend it without hesitation to both the producers and consumers of matrix theory." G.W. Stewart, SIAM Review
"There are three reasons why Horn and Johnson's new book Topics in Matrix Analysis and its predecessor Matrix Analysis are indispensable. First, the authors cover their topics in depth. Second, they cover nonstandard topics. Third, they organize their material in the style of a textbook. Compared to an encyclopedia, they are more selective and more detailed; compared to exhaustive treatises, they are less selective and less detailed. Horn and Johnson establish a middle ground where they come much more than half way in meeting the reader who wants to do something with linear algebra." Bulletin of the International Linear Algebra Society
"There is no doubt that this two volume work, Matrix Analysis and Topics in Matrix Analysis is an important and unique contribution to the contemporary book literature on matrix theory." Marvin Marcus, Bulletin of the American Mathematical Society
"I can recommend it without hesitation to both the producers and consumers of matrix theory." G.W. Stewart, SIAM Review
"There are three reasons why Horn and Johnson's new book Topics in Matrix Analysis and its predecessor Matrix Analysis are indispensable. First, the authors cover their topics in depth. Second, they cover nonstandard topics. Third, they organize their material in the style of a textbook. Compared to an encyclopedia, they are more selective and more detailed; compared to exhaustive treatises, they are less selective and less detailed. Horn and Johnson establish a middle ground where they come much more than half way in meeting the reader who wants to do something with linear algebra." Bulletin of the International Linear Algebra Society
Book Description
Building on the foundations of its predecessor volume, this book treats in detail several topics with important applications and of special mathematical interest in matrix theory not included in the previous text. A background in elementary linear algebra and knowledge of rudimentary analytical concepts is assumed.
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18 of 19 people found the following review helpful:
5.0 out of 5 stars
A great reference source for advanced matrix analysis,
This review is from: Topics in Matrix Analysis (Paperback)
Horn and Johnson's MATRIX ANALYSIS AND TOPICS IN MATRIX ANALYSIS are true classics (like Knuth's Art of Computer Programming). You will find classic theorems and lemmas in matrix theory and linear algebra here along with their proofs (some of these are not found elsewhere).TOPICS IN MATRIX ANALYSIS contains a lot of stuff including LMI's, Kronecker and Hadamard products of matrices and their properties etc. I found this book indispensible when I was studying Semidefinite Programming. Both these books are now available in paperback (cost around 30+) dollars each. I have recently purchased both copies and can only strongly recommend them to anyone else.
1 of 1 people found the following review helpful:
5.0 out of 5 stars
This book is perfect for communication engineers,
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This review is from: Topics in Matrix Analysis (Paperback)
If you are communication engineer and exploring the world of channel estimation, MIMO, etc. and you need to understand the mathematical approach, you need this book. The book covers the SVD issue, which is most important for many applications.
1 of 1 people found the following review helpful:
5.0 out of 5 stars
Excellent for Matrix Analysis,
By
This review is from: Topics in Matrix Analysis (Paperback)
This book is an excellent reference for researchers in the fields of Matrix Analysis, Numerical Analysis, Theoretical Linear Algebra, etc. I am doing currently some research involving Matrix functions and generalizations of M-matrices and I use this book all the time. Some important features of this book include the facts that 1) it is well-written 2) It is clear 3) It very useful to researchers and graduate students. It is one of those books which you can't stop reading once you start.
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Inside This Book
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First Sentence:
The spectrum of a Matrix is a discrete point set; while the field of values can be a continuum, it is always a compact convex set. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
convex matrix function, monotone matrix function, similarity invariance property, positive stable matrices, spectral containment property, majorization inequalities, given matrix norm, majorization relationship, open real interval, ordered singular values, positive main diagonal entries, interlacing inequalities, numerical radius, sum matrix norm, triangularization theorem, unitarily invariant norm, symmetric gauge function, multiplicative commutator, additive commutator, singular value inequalities, weak majorization, unitary invariance, simple closed rectifiable curve, nonnegative diagonal matrix, principal submatrix Key Phrases - Capitalized Phrases (CAPs): (learn more)
Linear Algebra Appl, Further Readings, Linear Multilinear Algebra, Proof Let, National Acad, Acta Sci, Deduce Theorem, Sufficiency of Weyl New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The spectrum of a Matrix is a discrete point set; while the field of values can be a continuum, it is always a compact convex set. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
convex matrix function, monotone matrix function, similarity invariance property, positive stable matrices, spectral containment property, majorization inequalities, given matrix norm, majorization relationship, open real interval, ordered singular values, positive main diagonal entries, interlacing inequalities, numerical radius, sum matrix norm, triangularization theorem, unitarily invariant norm, symmetric gauge function, multiplicative commutator, additive commutator, singular value inequalities, weak majorization, unitary invariance, simple closed rectifiable curve, nonnegative diagonal matrix, principal submatrix Key Phrases - Capitalized Phrases (CAPs): (learn more)
Linear Algebra Appl, Further Readings, Linear Multilinear Algebra, Proof Let, National Acad, Acta Sci, Deduce Theorem, Sufficiency of Weyl New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 73
books:
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100
books
cite this book:
See all 100 books citing this book
- Matrix Analysis by Roger A. Horn on page 489, Back Matter (1), and Back Matter (2)
- Linear Algebra (2nd Edition) by Kenneth M Hoffman on page 133, page 231, and Back Matter
- Numerical Analysis (Proceedings of Symposia in Applied Mathematics, V. 22) by American Mathematical Society in Back Matter (1), and Back Matter (2)
- Linear Algebra (Electronic Companions) by David Carlson on page 77, and Back Matter
- Perturbation Theory for Linear Operators (Classics in Mathematics) by Tosio Kato in Back Matter
See all 73 books this book cites
- Space-Time Adaptive Processing for Radar (Artech House Radar Library) by J. R. Guerci on 5 pages
- Linear Algebra Gems: Assets for Undergraduate Mathematics (Notes Series, Volume 59) by Charles Johnson on 4 pages
- Matrix Analysis (Graduate Texts in Mathematics) by Rajendra Bhatia on 4 pages
- Positive Definite Matrices (Princeton in Applied Mathematics) by Rajendra Bhatia on page 32, page 196, and Back Matter
- Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications (Applied Optimization) by E. de Klerk in Front Matter, and Back Matter
See all 100 books citing this book
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