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Product Description

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.

Review

"The second edition of Matrix Analysis, as curated by Roger Horn and Charlie Johnson, is the definitive source and indispensable reference for the foundations of matrix analysis. The material is comprehensive yet thoughtfully collected, and presented with insightful exposition and crystal-clear organization. This book is for anyone who comes in contact with matrices, be it applied scientist, casual user, or experienced researcher."
Ilse Ipsen, North Carolina State University

"The second edition of Matrix Analysis by Horn and Johnson is a significant enhancement (featuring a large number of recent research results, new and illuminating approaches, a comprehensive summary of basic linear algebra and matrix theory, hints on some problems, and a highly detailed index) of the hugely successful and widely used first edition. It is a monumental contribution on the theory and applications of matrices. I had the honor of using some chapters of the draft of the second edition in my Advanced Matrix Analysis class at Georgia State University. I am certain that the second edition of Matrix Analysis will be the standard graduate textbook and an indispensable reference book on matrix theory for many years to come."
Zhongshan Li, Georgia State University

"The book is well organized, completely readable, and very enlightening. For researchers in matrix analysis, matrix computations, applied linear algebra, or computational science, this second edition is a valuable book."
Jesse L. Barlow, Computing Reviews

"The book is a valuable modern textbook devoted to the fundamentals of this active area of research, having many applications in mathematics and other disciplines. The book is clearly and carefully edited. The book is useful for graduate students, researchers and any person who loves matrix analysis."
Mohammad Sal Moslehian, Mathematical Reviews

"With the additional material and exceedingly clear exposition, this book will remain the go-to book for graduate students and researchers alike in the area of linear algebra and matrix theory. I suspect there are few readers who will go through this book and not learn many new things. It is an invaluable reference for anyone working in this area."
Anne Greenbaum, SIAM Review

"The new edition is clearly a must-have for anyone seriously interested in matrix analysis."
Nick Higham, Applied Mathematics, Software and Workflow blog

Book Description

The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises.

About the Author

Roger A. Horn is a Research Professor in the Department of Mathematics at the University of Utah. He is co-author of Topics in Matrix Analysis (Cambridge University Press, 1994).

Charles R. Johnson is a Professor in the Department of Mathematics at the College of William and Mary. He is co-author of Topics in Matrix Analysis (Cambridge University Press, 1994).

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Customer reviews

4.5 out of 54.5 out of 5
60 global ratings

Top reviews from the United States

ericw95
5.0 out of 5 starsVerified Purchase
Great read and reference book, but not for the Introductory Level Reader
Reviewed in the United States on October 8, 2019
This textbook is extremely effective if you already have a decent foundation in linear algebra. The theorems, lemmas, corollaries, and approach taken are fairly rigorous, and are right in line with what one would expect from a Matrix Analysis course textbook. While it is a... See more
This textbook is extremely effective if you already have a decent foundation in linear algebra. The theorems, lemmas, corollaries, and approach taken are fairly rigorous, and are right in line with what one would expect from a Matrix Analysis course textbook. While it is a rather difficult read as the subject material doesn''t come naturally to people like me, the proofs are largely well lain out and presented as intuitively as really can be expected, and the book is largely self-contained. None of the BS "This result is obvious/too trivial", etc (which is all too familiar once you get past introductory mathematics material, so this was a welcome surprise). Furthermore, the book proves most of the major results, and does not reference you to unproven claims or assertions frequently (I can remember maybe a dozen at most proofs out of a few hundred total that referenced exercises that were not explicitly proven in the book). While the book is self-contained, much of the introductory material is presented extremely abruptly and tersely just to serve as a reference, so this book is not for someone who hasn''t touched Linear Algebra since Lin Alg 101. I would recommend brushing up on introductory material before jumping in; particularly, on all of the material in Section 0 (which you can find in the preview of the book here on Amazon). If you have a firm grasp of Section 0 going in, the book will be very helpful for you. As the book contains most major theorems related to matrices in some form, it also makes a great reference text once you''ve finished.
6 people found this helpful
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Randall Reese
3.0 out of 5 starsVerified Purchase
Decent book with horrible format
Reviewed in the United States on January 24, 2014
I think that while this book has great concepts and exercises in it, the format that these are presented is a bit bulksome and very difficult to read. His method of numbering is horrible. He has exercises (unnumbered), problems (numbered), theorems (numbered) and statements... See more
I think that while this book has great concepts and exercises in it, the format that these are presented is a bit bulksome and very difficult to read. His method of numbering is horrible. He has exercises (unnumbered), problems (numbered), theorems (numbered) and statements (numbered in a different format than the theorems). Finding anything in the book is a nightmare. Referring to a concept in the book usually requires something like "Go to the 45th page and then find the 3rd exercise from the bottom (exercises have no number remember). There is a line above that with the statement that you need." The whole book could use a major format overhaul. Then it would be a 5 star book.
10 people found this helpful
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kaneda
3.0 out of 5 starsVerified Purchase
Kindle edition review... great material but many printing mistakes in the kindle edition
Reviewed in the United States on April 22, 2014
I''d give this 5 stars if all the printing mistakes were eliminated (things like missing square root signs). I guess they''re still trying to get the kinks out of the kindle electronic format. I assume these problems are not there in the regular printed edition, but I don''t... See more
I''d give this 5 stars if all the printing mistakes were eliminated (things like missing square root signs). I guess they''re still trying to get the kinks out of the kindle electronic format. I assume these problems are not there in the regular printed edition, but I don''t know.

The material itself is great... very thorough. Perfect for some who has taken an introductory linear algebra course already. Plenty of exercises.
2 people found this helpful
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Felipe Campos
5.0 out of 5 starsVerified Purchase
Beautiful
Reviewed in the United States on September 20, 2018
One of the finest math books I have encountered. Very deep, complete and with a outstanding amount of excercises.
One person found this helpful
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Michael Thoreau
4.0 out of 5 starsVerified Purchase
In depth but definitely a Maths textbook
Reviewed in the United States on October 1, 2020
Wouldn''t recommend for engineers afraid to get in to the maths.
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Shuhua
5.0 out of 5 starsVerified Purchase
good
Reviewed in the United States on February 6, 2020
a bible for matrix analysis
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jacob
5.0 out of 5 starsVerified Purchase
Very good
Reviewed in the United States on September 1, 2013
I am using this book for a course right now and I love it. I have taken 2 other linear algebra courses and the chapter 0 (review of linear algebra) of this book is so so much better than any of the other books I used. I have nothing to compare the other chapters to but I... See more
I am using this book for a course right now and I love it. I have taken 2 other linear algebra courses and the chapter 0 (review of linear algebra) of this book is so so much better than any of the other books I used. I have nothing to compare the other chapters to but I really like it so far. I haven''t gone through the entire book yet but for any professors out there wondering, your students should like this book.
4 people found this helpful
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Amazon Customer
5.0 out of 5 starsVerified Purchase
Five Stars
Reviewed in the United States on September 19, 2015
It is really good source.
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Top reviews from other countries

Amazon Customer
5.0 out of 5 starsVerified Purchase
Full Matrix Analysis with theorem treatment proof
Reviewed in the United Kingdom on September 29, 2019
Must say this is one of the best books that I have come across in Matrix analysis which comes with theorem and proofs with a very nice clear print that makes it absolutely a must have book for any undergraduate, postgraduate and beyond used in almost in any scientific and...See more
Must say this is one of the best books that I have come across in Matrix analysis which comes with theorem and proofs with a very nice clear print that makes it absolutely a must have book for any undergraduate, postgraduate and beyond used in almost in any scientific and engineering dicipline. Thank you, you saved me a lot of time searching the net and book stores.
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Nicola Mastronardi
5.0 out of 5 starsVerified Purchase
Five Stars
Reviewed in the United Kingdom on July 9, 2016
tHE BOOK IS IN EXCELLENT CONDITIONS
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Isheteyak
5.0 out of 5 starsVerified Purchase
Great for pure mathematicians.
Reviewed in India on March 10, 2021
Excellent book on matrix theory. Author assumes the basic knowledge of linear algebra like vector spaces, linear transformations and other elementary concepts. The book is very well written. It is for pure mathematics student. It might be of help to physicists or engineers...See more
Excellent book on matrix theory. Author assumes the basic knowledge of linear algebra like vector spaces, linear transformations and other elementary concepts. The book is very well written. It is for pure mathematics student. It might be of help to physicists or engineers but it''s applicability if limited for they don''t have to know every result or theorems concerning the matrices as provided in the book. For a mathematics students or researchers this book is really good almost all the theory (definitions, theorems etc) has been explained clearly. At the end of every section there''s problem set which ranges from very easy which are immediate consequence of results given in the section to tough which requires your considerable amount of time and mind. Many problems are based on physics, statistics or other disciplines which, I think, can be left if not interested. Sections on positive definite matrices and positive matrices are what I found most well written.
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Mr. Raymond L. Hall
3.0 out of 5 starsVerified Purchase
Pure Mathematics Only.
Reviewed in Australia on September 14, 2020
OK if one is a pure mathematician, but far too detailed for an engineer or physicist. Layout forbidding and sleep inducing. I would not not have purchased this had a few pages been available for viewing.
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mmcguire
5.0 out of 5 starsVerified Purchase
Classic text
Reviewed in Canada on August 8, 2013
This is a later version of a classic text on Matrix Operations. For communications and signal processing research, this textbook is almost essential. In particular, for work on Multiple-Input Multiple-Output (MIMO) communications systems, there are a lot of useful theorems...See more
This is a later version of a classic text on Matrix Operations. For communications and signal processing research, this textbook is almost essential. In particular, for work on Multiple-Input Multiple-Output (MIMO) communications systems, there are a lot of useful theorems and properties to be found in this book.
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