Download e-book for kindle: Algebraic and Computational Aspects of Real Tensor Ranks by Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki

By Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki

This e-book presents accomplished summaries of theoretical (algebraic) and computational facets of tensor ranks, maximal ranks, and usual ranks, over the true 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 purposes in records. The e-book offers numerous attention-grabbing principles, together with determinant polynomials, determinantal beliefs, totally nonsingular tensors, totally complete column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. as well as studies of the way to be certain genuine tensor ranks in information, international theories similar to the Jacobian procedure also are reviewed in info. The booklet contains besides an obtainable and accomplished advent of mathematical backgrounds, with fundamentals of optimistic polynomials and calculations by utilizing the Groebner foundation. in addition, this publication presents 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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