Plane Stochastic Tensors

Maolin Che and Yimin Wei
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Maolin Che: Southwestern University of Finance and Economics, School of Economics Mathematics
Yimin Wei: Fudan University, School of Mathematical Sciences

Chapter Chapter 5 in Theory and Computation of Complex Tensors and its Applications, 2020, pp 117-146 from Springer

Abstract: Abstract We study combinatorial properties of nonnegative tensors. We make the following contributions: (1) we obtain equivalent conditions for sign nonsingular tensors and relationships between the combinatorial determinant and the permanent of nonnegative tensors, in Theorems 5.2.1 and 5.2.2; (2) the sets of plane stochastic tensors and totally plane stochastic tensors are closed, bounded and convex sets, and an nonnegative tensor has a plane stochastic pattern if and only if its positive entries are contained in a positive diagonal, in Lemma 5.3.1 and Theorem 5.3.2; (3) from a nonnegative tensor, we propose a normalization algorithm which converges to a plane stochastic tensor, in Theorem 5.3.8; (4) we discuss the boundlessness of the diagonal products of any nonnegative tensor and obtain a probabilistic algorithm after Theorem 5.4.4 for locating a positive diagonal in a (0, 1)-tensor; (5) we explore the axial N-index assignment problem via the set of plane stochastic tensors in Sect. 5.5.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-15-2059-4_5

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DOI: 10.1007/978-981-15-2059-4_5

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