Download PDF by Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki: Algebraic and Computational Aspects of Real Tensor Ranks

By Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki

ISBN-10: 4431554580

ISBN-13: 9784431554585

This e-book presents complete summaries of theoretical (algebraic) and computational points of tensor ranks, maximal ranks, and usual ranks, over the true quantity box. even though tensor ranks were usually argued within the advanced quantity box, it's going to be emphasised that this e-book treats actual tensor ranks, that have direct functions in data. The e-book presents numerous fascinating principles, together with determinant polynomials, determinantal beliefs, completely nonsingular tensors, totally complete column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. as well as studies of easy methods to verify genuine tensor ranks in info, international theories resembling the Jacobian procedure also are reviewed in information. The e-book contains to boot an available and complete advent of mathematical backgrounds, with fundamentals of optimistic polynomials and calculations through the use of the Groebner foundation. in addition, this publication offers insights into numerical equipment of discovering tensor ranks via simultaneous singular price decompositions.

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Algebraic and Computational Aspects of Real Tensor Ranks (SpringerBriefs in Statistics) by Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki

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