By Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki

ISBN-10: 4431554580

ISBN-13: 9784431554585

This booklet presents entire summaries of theoretical (algebraic) and computational points of tensor ranks, maximal ranks, and standard ranks, over the genuine quantity box. even supposing tensor ranks were usually argued within the complicated quantity box, it may be emphasised that this ebook treats genuine tensor ranks, that have direct functions in records. The booklet offers numerous fascinating principles, together with determinant polynomials, determinantal beliefs, completely nonsingular tensors, completely complete column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. as well as stories of how to make certain actual tensor ranks in info, worldwide theories equivalent to the Jacobian technique also are reviewed in information. The publication comprises to boot an available and entire advent of mathematical backgrounds, with fundamentals of optimistic polynomials and calculations through the use of the Groebner foundation. additionally, this booklet presents insights into numerical tools 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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