07653nam 2201777 450 991082064220332120230803203024.01-4008-5274-910.1515/9781400852741(CKB)3710000000128520(EBL)1689375(OCoLC)881568749(SSID)ssj0001228549(PQKBManifestationID)12476106(PQKBTitleCode)TC0001228549(PQKBWorkID)11167903(PQKB)11600707(MiAaPQ)EBC1689375(StDuBDS)EDZ0000989992(DE-B1597)447973(OCoLC)979742471(DE-B1597)9781400852741(Au-PeEL)EBL1689375(CaPaEBR)ebr10884735(CaONFJC)MIL619589(EXLCZ)99371000000012852020140704h20142014 uy 0engur|n|---|||||txtccrTopics in quaternion linear algebra /Leiba RodmanCourse BookPrinceton, New Jersey ;Oxfordshire, England :Princeton University Press,2014.©20141 online resource (379 p.)Princeton Series in Applied MathematicsDescription based upon print version of record.0-691-16185-2 Includes bibliographical references and index.Front matter --Contents --Preface --Chapter One. Introduction --Chapter Two. The algebra of quaternions --Chapter Three. Vector spaces and matrices: Basic theory --Chapter Four. Symmetric matrices and congruence --Chapter Five. Invariant subspaces and Jordan form --Chapter Six. Invariant neutral and semidefinite subspaces --Chapter Seven. Smith form and Kronecker canonical form --Chapter Eight. Pencils of hermitian matrices --Chapter Nine. Skewhermitian and mixed pencils --Chapter Ten. Indefinite inner products: Conjugation --Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution --Chapter Twelve. Mixed matrix pencils: Nonstandard involutions --Chapter Thirteen. Indefinite inner products: Nonstandard involution --Chapter Fourteen. Matrix equations --Chapter Fifteen. Appendix: Real and complex canonical forms --Bibliography --IndexQuaternions 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 It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and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.Princeton series in applied mathematics.Algebras, LinearTextbooksQuaternionsTextbooksCholesky factorization.Hamiltonian matrices.Jordan canonical form.Jordan form.Kronecker canonical form.Kronecker form.Kronecker forms.Schur triangularization theorem.Smith form.Sylvester equation.algebraic Riccati equations.antiautomorphisms.automorphisms.bilateral quadratic equations.boundedness.canonical forms.complex hermitian matrices.complex matric pencils.complex matrices.complex matrix polynomials.congruence.conjugation.conventions.determinants.diagonal form.diagonalizability.differential equations.dissipative matrices.eigenvalues.eigenvectors.equivalence.expansive matrices.hermitian inner product.hermitian matrices.hermitian matrix pencils.hermitian pencils.indefinite inner products.inertia theorems.invariant Langragian subspaces.invariant Langrangian subspaces.invariant neutral subspaces.invariant semidefinite subspaces.invariant subspaces.involutions.linear quadratic regulators.matrix algebra.matrix decompositions.matrix equations.matrix pencils.matrix polynomials.maximal invariant semidefinite subspaces.metric space.mixed matrix pencils.mixed pencils.mixed quaternion matrix pencils.neutral subspaces.nondegenerate.nonstandard involution.nonstandard involutions.nonuniqueness.notations.numerical cones.numerical ranges.pencils.polynomial matrix equations.quadratic maps.quaternion algebra.quaternion coefficients.quaternion linear algebra.quaternion matrices.quaternion matrix pencils.quaternion subspaces.quaternions.real linear transformations.real matrices.real matrix pencils.real matrix polynomials.real symmetric matrices.root subspaces.scalar quaternions.semidefinite subspaces.skew-Hamiltonian matrices.skewhermitian inner product.skewhermitian matrices.skewhermitian pencils.skewsymmetric matrices.square-size quaternion matrices.standard matrices.symmetric matrices.symmetries.symmetry properties.unitary matrices.vector spaces.Algebras, LinearQuaternions512/.5SK 230rvkRodman L.54260MiAaPQMiAaPQMiAaPQBOOK9910820642203321Topics in quaternion linear algebra3960591UNINA