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Matrix Mathematics: Theory, Facts, and Formulas

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Matrix Mathematics: Theory, Facts, and Formulas

4.85 58,364 ratings · 6,674 reviews
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Overview: When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices.Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations, Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms. Covers hundreds of important and useful results on matrix theory, many never before available in any book Provides a list of symbols and a summary of conventions for easy use Includes an extensive collection of scalar identities and inequalities Features a detailed bibliography and author index with page references Includes an exhaustive subject index with cross-referencing

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Pages N/A
Language Eng
Published January 1, 2009
ISBN 8188436
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Dennis S. Bernstein
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Dennis S. Bernstein is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Dennis S. Bernstein can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
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Anthony Anderson August 15, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Gary Collins May 18, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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James Smith May 25, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Jacob Collins
Jacob Collins September 08, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
George King
George King March 15, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Michelle Lopez
Michelle Lopez September 11, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Joshua Lopez
Joshua Lopez June 06, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Thomas Reyes October 08, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Elizabeth  Parker
Elizabeth Parker July 24, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Mary Garcia
Mary Garcia July 21, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Ryan Rivera
Ryan Rivera August 03, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Margaret Flores
Margaret Flores May 13, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Kimberly Adams
Kimberly Adams April 12, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Linda Thomas
Linda Thomas June 07, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Jennifer Nelson August 04, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Elizabeth Clark
Elizabeth Clark February 26, 2025
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Sharon Evans
Sharon Evans July 26, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Donna Lee
Donna Lee March 09, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Rebecca Hill
Rebecca Hill January 03, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
John Edwards
John Edwards December 02, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Nancy Robinson
Nancy Robinson August 13, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Nicholas Diaz
Nicholas Diaz August 18, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Christopher Diaz
Christopher Diaz August 04, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Linda Hall
Linda Hall August 25, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Paul Mitchell
Paul Mitchell June 22, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Anthony Robinson
Anthony Robinson September 17, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Cynthia Turner
Cynthia Turner March 21, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Lisa Allen
Lisa Allen December 23, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Gary King
Gary King June 22, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Anthony Phillips
Anthony Phillips August 09, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Joshua Baker
Joshua Baker November 27, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Elizabeth Young
Elizabeth Young September 23, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Kenneth Wright
Kenneth Wright January 16, 2025
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Deborah Gonzalez
Deborah Gonzalez January 09, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Daniel Jackson
Daniel Jackson April 09, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Daniel Williams
Daniel Williams February 07, 2025
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
Ryan Phillips
Ryan Phillips June 15, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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