Get Algebraic and Computational Aspects of Real Tensor Ranks PDF

By Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki

This ebook offers finished summaries of theoretical (algebraic) and computational elements of tensor ranks, maximal ranks, and commonplace ranks, over the genuine quantity box. even supposing tensor ranks were frequently argued within the complicated quantity box, it's going to be emphasised that this e-book treats genuine tensor ranks, that have direct functions in facts. The booklet presents numerous fascinating 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 experiences of the way to ascertain actual tensor ranks in information, international theories equivalent to the Jacobian technique also are reviewed in information. The booklet contains besides an obtainable and complete creation of mathematical backgrounds, with fundamentals of optimistic polynomials and calculations by utilizing the Groebner foundation. moreover, this e-book 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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