LEADER 03838nam 22006854a 450 001 9910454726503321 005 20200520144314.0 010 $a1-282-12974-0 010 $a9786612129742 010 $a1-4008-2778-7 024 7 $a10.1515/9781400827787 035 $a(CKB)1000000000756263 035 $a(EBL)445446 035 $a(OCoLC)330822909 035 $a(SSID)ssj0000224738 035 $a(PQKBManifestationID)11910947 035 $a(PQKBTitleCode)TC0000224738 035 $a(PQKBWorkID)10210617 035 $a(PQKB)10076542 035 $a(MiAaPQ)EBC445446 035 $a(DE-B1597)446708 035 $a(OCoLC)979745018 035 $a(OCoLC)990529004 035 $a(DE-B1597)9781400827787 035 $a(PPN)170253570 035 $a(Au-PeEL)EBL445446 035 $a(CaPaEBR)ebr10284074 035 $a(CaONFJC)MIL212974 035 $a(EXLCZ)991000000000756263 100 $a20060714d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPositive definite matrices$b[electronic resource] /$fRajendra Bhatia 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$dc2007 215 $a1 online resource (265 p.) 225 1 $aPrinceton series in applied mathematics 300 $aDescription based upon print version of record. 311 $a0-691-16825-3 311 $a0-691-12918-5 320 $aIncludes bibliographical references (p. [237]-245) and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. Positive Matrices -- $tChapter Two. Positive Linear Maps -- $tChapter Three. Completely Positive Maps -- $tChapter Four. Matrix Means -- $tChapter Five. Positive Definite Functions -- $tChapter Six. Geometry of Positive Matrices -- $tBibliography -- $tIndex -- $tNotation 330 $aThis book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices. Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses. 410 0$aPrinceton series in applied mathematics. 606 $aMatrices 608 $aElectronic books. 615 0$aMatrices. 676 $a512.9/434 686 $aSK 220$2rvk 700 $aBhatia$b Rajendra$f1952-$059869 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454726503321 996 $aPositive definite matrices$91226929 997 $aUNINA