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

By Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki

This booklet offers entire summaries of theoretical (algebraic) and computational facets of tensor ranks, maximal ranks, and normal ranks, over the true quantity box. even if tensor ranks were frequently argued within the complicated quantity box, it's going to be emphasised that this ebook treats genuine tensor ranks, that have direct functions in facts. The ebook offers numerous attention-grabbing principles, 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 experiences of tips on how to be certain actual tensor ranks in information, international theories similar to the Jacobian procedure also are reviewed in info. The publication comprises besides an available and entire creation of mathematical backgrounds, with fundamentals of confident polynomials and calculations through the use of the Groebner foundation. additionally, this publication offers insights into numerical equipment of discovering tensor ranks via simultaneous singular worth decompositions.

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