LEADER 07653nam 2201777 450 001 9910820642203321 005 20230803203024.0 010 $a1-4008-5274-9 024 7 $a10.1515/9781400852741 035 $a(CKB)3710000000128520 035 $a(EBL)1689375 035 $a(OCoLC)881568749 035 $a(SSID)ssj0001228549 035 $a(PQKBManifestationID)12476106 035 $a(PQKBTitleCode)TC0001228549 035 $a(PQKBWorkID)11167903 035 $a(PQKB)11600707 035 $a(MiAaPQ)EBC1689375 035 $a(StDuBDS)EDZ0000989992 035 $a(DE-B1597)447973 035 $a(OCoLC)979742471 035 $a(DE-B1597)9781400852741 035 $a(Au-PeEL)EBL1689375 035 $a(CaPaEBR)ebr10884735 035 $a(CaONFJC)MIL619589 035 $a(EXLCZ)993710000000128520 100 $a20140704h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTopics in quaternion linear algebra /$fLeiba Rodman 205 $aCourse Book 210 1$aPrinceton, New Jersey ;$aOxfordshire, England :$cPrinceton University Press,$d2014. 210 4$dİ2014 215 $a1 online resource (379 p.) 225 1 $aPrinceton Series in Applied Mathematics 300 $aDescription based upon print version of record. 311 0 $a0-691-16185-2 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tPreface --$tChapter One. Introduction --$tChapter Two. The algebra of quaternions --$tChapter Three. Vector spaces and matrices: Basic theory --$tChapter Four. Symmetric matrices and congruence --$tChapter Five. Invariant subspaces and Jordan form --$tChapter Six. Invariant neutral and semidefinite subspaces --$tChapter Seven. Smith form and Kronecker canonical form --$tChapter Eight. Pencils of hermitian matrices --$tChapter Nine. Skewhermitian and mixed pencils --$tChapter Ten. Indefinite inner products: Conjugation --$tChapter Eleven. Matrix pencils with symmetries: Nonstandard involution --$tChapter Twelve. Mixed matrix pencils: Nonstandard involutions --$tChapter Thirteen. Indefinite inner products: Nonstandard involution --$tChapter Fourteen. Matrix equations --$tChapter Fifteen. Appendix: Real and complex canonical forms --$tBibliography --$tIndex 330 $aQuaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used. 410 0$aPrinceton series in applied mathematics. 606 $aAlgebras, Linear$vTextbooks 606 $aQuaternions$vTextbooks 610 $aCholesky factorization. 610 $aHamiltonian matrices. 610 $aJordan canonical form. 610 $aJordan form. 610 $aKronecker canonical form. 610 $aKronecker form. 610 $aKronecker forms. 610 $aSchur triangularization theorem. 610 $aSmith form. 610 $aSylvester equation. 610 $aalgebraic Riccati equations. 610 $aantiautomorphisms. 610 $aautomorphisms. 610 $abilateral quadratic equations. 610 $aboundedness. 610 $acanonical forms. 610 $acomplex hermitian matrices. 610 $acomplex matric pencils. 610 $acomplex matrices. 610 $acomplex matrix polynomials. 610 $acongruence. 610 $aconjugation. 610 $aconventions. 610 $adeterminants. 610 $adiagonal form. 610 $adiagonalizability. 610 $adifferential equations. 610 $adissipative matrices. 610 $aeigenvalues. 610 $aeigenvectors. 610 $aequivalence. 610 $aexpansive matrices. 610 $ahermitian inner product. 610 $ahermitian matrices. 610 $ahermitian matrix pencils. 610 $ahermitian pencils. 610 $aindefinite inner products. 610 $ainertia theorems. 610 $ainvariant Langragian subspaces. 610 $ainvariant Langrangian subspaces. 610 $ainvariant neutral subspaces. 610 $ainvariant semidefinite subspaces. 610 $ainvariant subspaces. 610 $ainvolutions. 610 $alinear quadratic regulators. 610 $amatrix algebra. 610 $amatrix decompositions. 610 $amatrix equations. 610 $amatrix pencils. 610 $amatrix polynomials. 610 $amaximal invariant semidefinite subspaces. 610 $ametric space. 610 $amixed matrix pencils. 610 $amixed pencils. 610 $amixed quaternion matrix pencils. 610 $aneutral subspaces. 610 $anondegenerate. 610 $anonstandard involution. 610 $anonstandard involutions. 610 $anonuniqueness. 610 $anotations. 610 $anumerical cones. 610 $anumerical ranges. 610 $apencils. 610 $apolynomial matrix equations. 610 $aquadratic maps. 610 $aquaternion algebra. 610 $aquaternion coefficients. 610 $aquaternion linear algebra. 610 $aquaternion matrices. 610 $aquaternion matrix pencils. 610 $aquaternion subspaces. 610 $aquaternions. 610 $areal linear transformations. 610 $areal matrices. 610 $areal matrix pencils. 610 $areal matrix polynomials. 610 $areal symmetric matrices. 610 $aroot subspaces. 610 $ascalar quaternions. 610 $asemidefinite subspaces. 610 $askew-Hamiltonian matrices. 610 $askewhermitian inner product. 610 $askewhermitian matrices. 610 $askewhermitian pencils. 610 $askewsymmetric matrices. 610 $asquare-size quaternion matrices. 610 $astandard matrices. 610 $asymmetric matrices. 610 $asymmetries. 610 $asymmetry properties. 610 $aunitary matrices. 610 $avector spaces. 615 0$aAlgebras, Linear 615 0$aQuaternions 676 $a512/.5 686 $aSK 230$2rvk 700 $aRodman$b L.$054260 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910820642203321 996 $aTopics in quaternion linear algebra$93960591 997 $aUNINA