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 ebook offers accomplished summaries of theoretical (algebraic) and computational features of tensor ranks, maximal ranks, and ordinary ranks, over the genuine quantity box. even if tensor ranks were usually argued within the advanced quantity box, it may be emphasised that this ebook treats actual tensor ranks, that have direct functions in statistics. The booklet offers numerous fascinating rules, together with determinant polynomials, determinantal beliefs, totally nonsingular tensors, completely complete column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. as well as stories of the way to be sure actual tensor ranks in info, international theories similar to the Jacobian procedure also are reviewed in info. The e-book contains besides an obtainable and accomplished creation of mathematical backgrounds, with fundamentals of optimistic polynomials and calculations by utilizing the Groebner foundation. moreover, this booklet offers insights into numerical equipment of discovering tensor ranks via simultaneous singular worth 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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