Advanced Topics in Linear Algebra: Weaving Matrix Problems through the Weyr Form

Description: Advanced Topics in Linear Algebra by John Clark, Kevin O'Meara, Charles Vinsonhaler This book develops the Weyr matrix canonical form, a largely unknown cousin of the Jordan form. It explores novel applications, including include matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry. Module theory and algebraic geometry are employed but with self-contained accounts. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a number of mathematical situations, yet it remains somewhat of a mystery, even to many who are skilled in linear algebra. Written in an engaging style, this book presents various advanced topics in linear algebra linked through the Weyr form. Kevin OMeara, John Clark, andCharles Vinsonhaler develop the Weyr form from scratch and include an algorithm for computing it. A fascinating duality exists between the Weyr form and the Jordan form. Developing an understanding ofboth forms will allow students and researchers to exploit the mathematical capabilities of each in varying situations. Weaving together ideas and applications from various mathematical disciplines, Advanced Topics in Linear Algebra is much more than a derivation of the Weyr form. It presents novel applications of linear algebra, such as matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry, with the latter two having topicalconnections to phylogenetic invariants in biomathematics and multivariate interpolation. Among the related mathematical disciplines from which the book draws ideas are commutative and noncommutative ringtheory, module theory, field theory, topology, and algebraic geometry. Numerous examples and current open problems are included, increasing the books utility as a graduate text or as a reference for mathematicians and researchers in linear algebra. Author Biography Kevin C. OMeara has taught and researched broadly within algebra, based mostly at the University of Canterbury, New Zealand, but with many visits to the University of Connecticut, USA. Linear algebra has been a recurring theme in much of his work, often in novel settings.John Clarks research interests are in the theory of rings and modules, starting with his PhD written under the supervision of Christian Jensen of the University of Copenhagen. Ring theory has continued to fascinate and surprise him during these last forty years.Charles I. Vinsonhaler has over 100 publications, most in algebra, a few in actuarial science and mathematics education. He coauthored a small book on problem solving with Tom DeFranco. He has held a number of visiting positions, including the University of Canterbury, NZ, where he was an Erskine Fellow. Table of Contents PrefaceChapter 1. Background Linear AlgebraChapter 2. The Weyr FormChapter 3. CentralizersChapter 4. The Module SettingChapter 5. Gerstenhabers TheoremChapter 6. Approximate Simultaneous DiagonalizationChapter 7. Algebraic VarietiesBibliography Review "The book covers both early and quite recent results, has informative remarks and thorough theoretical deductions, provides interesting footnotes and brief biographies of related mathematicians, and contains concrete and elegant proofs. Overall, the book is written in a self-contained, introductory, and inspiring fashion." Mathematical Reviews Long Description The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a number of mathematical situations, yet it remains somewhat of a mystery, even to many who are skilled in linear algebra. Written in an engaging style, this book presents various advanced topics in linear algebra linked through the Weyr form. Kevin OMeara, John Clark, andCharles Vinsonhaler develop the Weyr form from scratch and include an algorithm for computing it. A fascinating duality exists between the Weyr form and the Jordan form. Developing an understanding of both forms will allow students and researchers to exploit the mathematical capabilities of each invarying situations. Weaving together ideas and applications from various mathematical disciplines, Advanced Topics in Linear Algebra is much more than a derivation of the Weyr form. It presents novel applications of linear algebra, such as matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry, with the latter two having topical connections to phylogenetic invariants in biomathematics and multivariate interpolation. Among therelated mathematical disciplines from which the book draws ideas are commutative and noncommutative ring theory, module theory, field theory, topology, and algebraic geometry. Numerous examples and current open problems are included, increasing the books utility as a graduate text or as a reference formathematicians and researchers in linear algebra. Review Text "The book covers both early and quite recent results, has informative remarks and thorough theoretical deductions, provides interesting footnotes and brief biographies of related mathematicians, and contains concrete and elegant proofs. Overall, the book is written in a self-contained, introductory, and inspiring fashion." Mathematical Reviews Review Quote "The book covers both early and quite recent results, has informative remarks and thorough theoretical deductions, provides interesting footnotes and brief biographies of related mathematicians, and contains concrete and elegant proofs. Overall, the book is written in a self-contained, introductory, and inspiring fashion." Mathematical Reviews Feature Book should be ready for the Joint Mathematics Meetings (Jan 4-7, 2012)Selling point: Gives the only comprehensive account of the Weyr matrix canonical form and its applicationsSelling point: Many applications discussed have not appeared previously in book formSelling point: Links the Weyr form to module theory over a general noncommutative ring without finiteness conditions, as against the classical use of modules over principal ideal domains in the development of the Jordan formSelling point: Devotes an entire chapter to the algebraic geometry connections to the linear algebra problems Details ISBN0199793735 Author Charles Vinsonhaler Short Title ADVD TOPICS IN LINEAR ALGEBRA Language English ISBN-10 0199793735 ISBN-13 9780199793730 Media Book Format Hardcover DEWEY 512.5 Illustrations Yes Year 2011 Subtitle Weaving Matrix Problems through the Weyr Form Imprint Oxford University Press Inc Place of Publication New York Country of Publication United States UK Release Date 2011-10-13 Publication Date 2011-10-13 AU Release Date 2011-10-13 NZ Release Date 2011-10-13 US Release Date 2011-10-13 Pages 432 Publisher Oxford University Press Inc Audience Postgraduate, Research & Scholarly We've got this At The Nile, if you're looking for it, we've got it. 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