LEADER 03889nam 22006375 450 001 9910254062003321 005 20220415182256.0 010 $a4-431-55459-9 024 7 $a10.1007/978-4-431-55459-2 035 $a(CKB)3710000000617034 035 $a(EBL)4454275 035 $a(SSID)ssj0001653985 035 $a(PQKBManifestationID)16433171 035 $a(PQKBTitleCode)TC0001653985 035 $a(PQKBWorkID)14982336 035 $a(PQKB)10372585 035 $a(DE-He213)978-4-431-55459-2 035 $a(MiAaPQ)EBC4454275 035 $a(PPN)192770624 035 $a(EXLCZ)993710000000617034 100 $a20160318d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAlgebraic and computational aspects of real tensor ranks$b[electronic resource] /$fby Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki 205 $a1st ed. 2016. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2016. 215 $a1 online resource (112 p.) 225 1 $aJSS Research Series in Statistics,$x2364-0057 300 $aDescription based upon print version of record. 311 $a4-431-55458-0 320 $aIncludes bibliographical references and index. 327 $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 × ˇ ˇ ˇ × 2 Tensors. 330 $aThis book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through simultaneous singular value decompositions. 410 0$aJSS Research Series in Statistics,$x2364-0057 606 $aStatistics  606 $aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/S17020 606 $aStatistics and Computing/Statistics Programs$3https://scigraph.springernature.com/ontologies/product-market-codes/S12008 606 $aStatistics for Social Sciences, Humanities, Law$3https://scigraph.springernature.com/ontologies/product-market-codes/S17040 615 0$aStatistics . 615 14$aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 615 24$aStatistics and Computing/Statistics Programs. 615 24$aStatistics for Social Sciences, Humanities, Law. 676 $a515.63 700 $aSakata$b Toshio$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755814 702 $aSumi$b Toshio$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMiyazaki$b Mitsuhiro$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254062003321 996 $aAlgebraic and Computational Aspects of Real Tensor Ranks$91963835 997 $aUNINA