Linear algebra and matrix theory have long been fundamental tools in mathematical disciplines as well as fertile fields for research. In this book the authors present classical and recent results of matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematical science, but the necessary material has appeared only sporadically in the literature and in university curricula. As interest in applied mathematics has grown, the need for a text and reference offering a broad selection of topics in matrix theory has become apparent, and this book meets that need. This volume reflects two concurrent views of matrix analysis. First, it encompasses topics in linear algebra that have arisen out of the needs of mathematical analysis. Second, it is an approach to real and complex linear algebraic problems that does not hesitate to use notions from analysis. Both views are reflected in its choice and treatment of topics.
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Book Description
Editorial Reviews
Review
"There seems little doubt that the book will become a standard reference for research workers in numerical mathematics." Computing Reviews
"The reviewer strongly recommends that those working in either pure or applied linear algebra have this book on their desks." SIAM Review
"The presentation is straightforward and extremely readable. The authors' enthusiasm pervades the book, and the printing is what we expect from this publisher. This will doubtless be the standard text for years to come." American Scientist
"The reviewer strongly recommends that those working in either pure or applied linear algebra have this book on their desks." SIAM Review
"The presentation is straightforward and extremely readable. The authors' enthusiasm pervades the book, and the printing is what we expect from this publisher. This will doubtless be the standard text for years to come." American Scientist
Book Description
A presentation of classical as well as recent results of matrix analysis that have proven important to applied mathematics and reflect two concurrent views of the subject.
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Most Helpful Customer Reviews
31 of 33 people found the following review helpful:
5.0 out of 5 stars
Excellent book.... for the initiated,
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This review is from: Matrix Analysis (Paperback)
Horn and Johnson has written an excellent reference book on somewhat-advanced linear algebra (from the point of view of an engineer). There's a lot of treasures in this book, but this book is NOT for beginning linear algebra. Rather, it is written as a handy reference to review and learn certain topics in linear algebra.Nonetheless, I really like their take on linear algebra. They motivate you in every subject and problem (for example, the relations between eigenvectors, eigenvalues, and optimization problems). These insights are invaluable and definitely worth the admission price. Together with Golub and Van Loan's "Matrix Computations", this is THE linear algebra book to get, although only if you're sufficiently initiated.
12 of 14 people found the following review helpful:
5.0 out of 5 stars
The most comprehensive and up-to-date reference/textbook.,
By
This review is from: Matrix Analysis (Paperback)
If you need to know anything about matrices - this is the book. It cover all the basic theory. Perfect for graduate-level courses. The book also has lots of material relevant to optimization theory and can be used in Operations Research courses. One of the nice features is a comprehensive index that makes the book a perfect reference source. Nicely written and easy to read.
10 of 13 people found the following review helpful:
5.0 out of 5 stars
An encyclopedic reference for matrix analysis and linear alg,
This review is from: Matrix Analysis (Paperback)
Horn and Johnson's MATRIX ANALYSIS is simply a masterpiece. You can find each and every result in matrix analysis along with it's proof in this book. Look at their companion volume "Topics in Matrix Analysis" too. Some of these results cannot be found elsewhere.
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First Sentence:
The purpose of this chapter is to catalog briefly, without proof, a number of useful concepts and facts, many of which implicity or explicity underlie the material covered in the main portion of the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
compatible vector norm, upper triangularizability, given matrix norm, real normal matrix, real orthogonal similarity, symmetric gauge function, invariant matrix norm, unitary diagonalization, triangularization theorem, unitarily invariant norm, main diagonal entries, interlacing inequalities, numerical radius, given vector norm, algebraically simple eigenvalue, distinct singular values, two given matrices, complex symmetric matrices, permutation similarity, irreducible nonnegative matrix, ordered singular values, complex symmetric matrix, given nonzero vector, orthonormal rows, monotone norm Key Phrases - Capitalized Phrases (CAPs): (learn more)
Further Readings, Linear Algebra Appl, Von Neumann, Prove Corollary, Prove Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The purpose of this chapter is to catalog briefly, without proof, a number of useful concepts and facts, many of which implicity or explicity underlie the material covered in the main portion of the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
compatible vector norm, upper triangularizability, given matrix norm, real normal matrix, real orthogonal similarity, symmetric gauge function, invariant matrix norm, unitary diagonalization, triangularization theorem, unitarily invariant norm, main diagonal entries, interlacing inequalities, numerical radius, given vector norm, algebraically simple eigenvalue, distinct singular values, two given matrices, complex symmetric matrices, permutation similarity, irreducible nonnegative matrix, ordered singular values, complex symmetric matrix, given nonzero vector, orthonormal rows, monotone norm Key Phrases - Capitalized Phrases (CAPs): (learn more)
Further Readings, Linear Algebra Appl, Von Neumann, Prove Corollary, Prove Theorem 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 49
books:
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100
books
cite this book:
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- Linear Algebra by Jin Ho Kwak on page 218, and page 256
- Total Positivity, Volume One by Samuel Karlin in Back Matter
- Matrix Methods for Engineers and Scientists by S. Barnett in Back Matter
- The Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin in Back Matter
- Finite-Dimensional Vector Spaces by P.R. Halmos in Back Matter
See all 49 books this book cites
- Numerical Methods for Linear Control Systems by Biswa Datta on 4 pages
- Algebra and Its Applications (Contemporary Mathematics) by Dinh V. Huynh on page 182, page 183, and page 200
- MIMO System Technology for Wireless Communications (Electrical Engineering & Applied Signal Processing Series) by George Tsoulos on page 111, and page 172
- Optimization: Theory and Practice by M.C. Joshi on page 48, and page 173
- Digital Controller Implementation and Fragility by Robert Istepanian on page 159, and page 248
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