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

By Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki

This booklet presents finished summaries of theoretical (algebraic) and computational points of tensor ranks, maximal ranks, and average ranks, over the true quantity box. even though tensor ranks were usually argued within the advanced quantity box, it's going to be emphasised that this e-book treats actual tensor ranks, that have direct purposes in statistics. The ebook offers a number of 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 studies of how you can ensure actual tensor ranks in information, international theories similar to the Jacobian approach also are reviewed in information. The e-book contains besides an available and finished creation of mathematical backgrounds, with fundamentals of confident polynomials and calculations through the use of the Groebner foundation. moreover, this e-book presents insights into numerical tools 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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