Advanced topics in linear algebra : weaving matrix problems through the Weyr Form
 Author/Creator
 O'Meara, Kevin C.
 Language
 English.
 Imprint
 Oxford ; New York : Oxford University Press, c2011.
 Physical description
 xxii, 400 p. : ill. ; 25 cm.
Access
Available online

Stacks

Unknown
QA184.2 .O44 2011

Unknown
QA184.2 .O44 2011
More options
Contributors
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [384]389) and index.
 Contents

 Preface  Chapter 1. Background Linear Algebra  Chapter 2. The Weyr Form  Chapter 3. Centralizers  Chapter 4. The Module Setting  Chapter 5. Gerstenhaber's Theorem  Chapter 6. Approximate Simultaneous Diagonalization  Chapter 7. Algebraic Varieties  Bibliography.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 ringtheoretically 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 selfcontained accounts of the nontrivial 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Algebras, Linear.
Bibliographic information
 Publication date
 2011
 Responsibility
 Kevin C. O'Meara, John Clark, Charles I. Vinsonhaler.
 ISBN
 9780199793730
 0199793735