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Advanced Topics in Linear Algebra: Weaving Matrix Problems Through the Weyr Form
Contributor(s): O'Meara, Kevin (Author), Clark, John (Author), Vinsonhaler, Charles (Author)
ISBN: 0199793735     ISBN-13: 9780199793730
Publisher: Oxford University Press, USA
OUR PRICE:   $142.50  
Product Type: Hardcover
Published: September 2011
Qty:
Additional Information
BISAC Categories:
- Mathematics | Algebra - Linear
Dewey: 512.5
LCCN: 2011003565
Physical Information: 1.2" H x 6.3" W x 9.4" (1.45 lbs) 432 pages
 
Descriptions, Reviews, Etc.
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 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 form
and 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, and
algebraic 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.