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Topics in Quaternion Linear Algebra - Leiba Rodman

Topics in Quaternion Linear Algebra

(Autor)

Buch | Hardcover
384 Seiten
2014
Princeton University Press (Verlag)
978-0-691-16185-3 (ISBN)
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Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra.
The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Leiba Rodman is professor of mathematics at the College of William & Mary. His books include Matrix Polynomials, Algebraic Riccati Equations, and Indefinite Linear Algebra and Applications.

*FrontMatter, pg. i*Contents, pg. vii*Preface, pg. xi*Chapter One. Introduction, pg. 1*Chapter Two. The algebra of quaternions, pg. 9*Chapter Three. Vector spaces and matrices: Basic theory, pg. 28*Chapter Four. Symmetric matrices and congruence, pg. 64*Chapter Five. Invariant subspaces and Jordan form, pg. 83*Chapter Six. Invariant neutral and semidefinite subspaces, pg. 131*Chapter Seven. Smith form and Kronecker canonical form, pg. 153*Chapter Eight. Pencils of hermitian matrices, pg. 172*Chapter Nine. Skewhermitian and mixed pencils, pg. 194*Chapter Ten. Indefinite inner products: Conjugation, pg. 228*Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution, pg. 261*Chapter Twelve. Mixed matrix pencils: Nonstandard involutions, pg. 279*Chapter Thirteen. Indefinite inner products: Nonstandard involution, pg. 300*Chapter Fourteen. Matrix equations, pg. 328*Chapter Fifteen. Appendix: Real and complex canonical forms, pg. 339*Bibliography, pg. 353*Index, pg. 361

Erscheint lt. Verlag 24.8.2014
Reihe/Serie Princeton Series in Applied Mathematics
Verlagsort New Jersey
Sprache englisch
Maße 178 x 254 mm
Gewicht 936 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
ISBN-10 0-691-16185-2 / 0691161852
ISBN-13 978-0-691-16185-3 / 9780691161853
Zustand Neuware
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