Book by OMeara Kevin Clark John Vinsonhaler Charles
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"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 "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
Advanced Topics in Linear Algebra presents, in an engaging style, novel topics linked through the Weyr matrix canonical form, a largely unknown cousin of the Jordan canonical form discovered by Eduard Weyr in 1885. The book also develops much linear algebra unconnected to canonical forms, that has not previously appeared in book form. It presents common applications of Weyr form, including matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry, with the latter two having topical connections to phylogenetic invariants in biomathematics and multivariate interpolation. The Weyr form clearly outperforms the Jordan form in many situations, particularly where two or more commuting matrices are involved, due to the block upper triangular form a Weyr matrix forces on any commuting matrix.
In this book, the authors develop the Weyr form from scratch, and include an algorithm for computing it. The Weyr form is also derived ring-theoretically in an entirely different way to the classical derivation of the Jordan form. A fascinating duality exists between the two forms that allows one to flip back and forth and exploit the combined powers of each. The book weaves together ideas from various mathematical disciplines, demonstrating dramatically the variety and unity of mathematics. Though the book's main focus is linear algebra, it also draws upon ideas from commutative and noncommutative ring theory, module theory, field theory, topology, and algebraic geometry.
Advanced Topics in Linear Algebra offers self-contained accounts of the non-trivial results used from outside linear algebra, and lots of worked examples, thereby making it accessible to graduate students. Indeed, the scope of the book makes it an appealing graduate text, either as a reference or for an appropriately designed one or two semester course. A number of the authors' previously unpublished results appear as well.
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Hardcover. Condición: new. Hardcover. 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 O'Meara, 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 book's utility as a graduate text or as a reference for mathematicians and researchers in linear algebra. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Nº de ref. del artículo: 9780199793730
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