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000754309 020__ $$a9784431554592$$q(electronic book)
000754309 020__ $$a4431554599$$q(electronic book)
000754309 020__ $$z9784431554585
000754309 0247_ $$a10.1007/978-4-431-55459-2$$2doi
000754309 035__ $$aSP(OCoLC)ocn945368362
000754309 035__ $$aSP(OCoLC)945368362
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000754309 049__ $$aISEA
000754309 050_4 $$aQA433
000754309 08204 $$a515/.63$$223
000754309 1001_ $$aSakata, Toshio,$$eauthor.
000754309 24510 $$aAlgebraic and computational aspects of real tensor ranks$$h[electronic resource] /$$cToshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki.
000754309 264_1 $$aTokyo :$$bSpringer,$$c2016.
000754309 300__ $$a1 online resource (viii, 108 pages) :$$billustrations.
000754309 336__ $$atext$$btxt$$2rdacontent
000754309 337__ $$acomputer$$bc$$2rdamedia
000754309 338__ $$aonline resource$$bcr$$2rdacarrier
000754309 4901_ $$aSpringerBriefs in statistics, JSS research series in statistics,$$x2191-544X
000754309 504__ $$aIncludes bibliographical references and index.
000754309 5050_ $$aBasics of Tensor Rank -- 3-Tensors -- Simple Evaluation Methods of Tensor Rank -- Absolutely Nonsingular Tensors and Determinantal Polynomials -- Maximal Ranks -- Typical Ranks -- Global Theory of Tensor Ranks -- 2 × 2 × · · · × 2 Tensors.
000754309 506__ $$aAccess limited to authorized users.
000754309 520__ $$aThis book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through simultaneous singular value decompositions.
000754309 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed March 22, 2016).
000754309 650_0 $$aCalculus of tensors.
000754309 650_0 $$aRanking and selection (Statistics)
000754309 7001_ $$aSumi, Toshio,$$eauthor.
000754309 7001_ $$aMiyazaki, Mitsuhiro,$$eauthor.
000754309 77608 $$iPrint version:$$z9784431554585
000754309 830_0 $$aSpringerBriefs in statistics.$$pJSS research series in statistics.
000754309 852__ $$bebk
000754309 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-4-431-55459-2$$zOnline Access$$91397441.1
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000754309 980__ $$aEBOOK
000754309 980__ $$aBIB
000754309 982__ $$aEbook
000754309 983__ $$aOnline
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