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

Hardcover | October 25, 2011

byKevin C. OMeara, John Clark, Charles I. Vinsonhaler

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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, and Charles Vinsonhaler develop the Weyr form from scratch and include an algorithm for computing it. A fascinating duality exists between the Weyr formand the Jordan form. Developing an understanding of both 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, andalgebraic geometry, with the latter two having topical connections to phylogenetic invariants in biomathematics and multivariate interpolation. Among the related 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 book's utility as a graduate text or as a reference for mathematicians and researchers in linear algebra.

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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 prese...

Kevin C. O'Meara has taught and researched broadly within algebra, based mostly at the University of Canterbury, New Zealand. John Clark's research interests are in the theory of rings and modules, starting with his Ph.D. written under the supervision of Christian Jensen of the University of Copenhagen. Ring theory has continued to fa...
Format:HardcoverDimensions:432 pages, 6.42 × 9.41 × 1.1 inPublished:October 25, 2011Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199793735

ISBN - 13:9780199793730

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Table of Contents

1. Background Linear Algebra2. The Weyr Form3. Centralizers4. The Module Setting5. Gerstenhaber's Theorem6. Approximate Simultaneous Diagonalization7. Algebraic Varieties