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

By Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki

ISBN-10: 4431554580

ISBN-13: 9784431554585

This booklet offers entire summaries of theoretical (algebraic) and computational features of tensor ranks, maximal ranks, and common ranks, over the genuine quantity box. even though tensor ranks were usually argued within the advanced quantity box, it may be emphasised that this publication treats genuine tensor ranks, that have direct functions in facts. The publication presents numerous attention-grabbing rules, 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 tips on how to ensure genuine tensor ranks in info, international theories equivalent to the Jacobian approach also are reviewed in information. The publication comprises besides an available and complete creation of mathematical backgrounds, with fundamentals of confident polynomials and calculations by utilizing the Groebner foundation. in addition, this publication 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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