Nonnegative tensors revisited: plane stochastic tensors

In this paper, we develop and enrich the theory of nonnegative tensors. We define the sign nonsingular tensors and establish the relationship between the combinatorial determinant and the permanent of nonnegative tensors. We generalize the results from doubly stochastic matrices to totally plane sto...

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Bibliographic Details
Published in:Linear & multilinear algebra Vol. 67; no. 7; pp. 1364 - 1391
Main Authors: Che, Maolin, Bu, Changjiang, Qi, Liqun, Wei, Yimin
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.07.2019
Taylor & Francis Ltd
Subjects:
Algorithms
Combinatorial analysis
combinatorial determinant
diagonal product
Lower bounds
Mathematical analysis
Nonnegative tensor
normalization algorithm
Operations research
plane stochastic tensors
positive diagonal
Quantum theory
sign nonsingular tensor
tensor permanent
Tensors
ISSN:0308-1087, 1563-5139
Online Access:Get full text
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Summary:In this paper, we develop and enrich the theory of nonnegative tensors. We define the sign nonsingular tensors and establish the relationship between the combinatorial determinant and the permanent of nonnegative tensors. We generalize the results from doubly stochastic matrices to totally plane stochastic tensors and obtain a probabilistic algorithm for locating a positive diagonal in a nonnegative tensor under certain conditions. We form a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors. We obtain a lower bound for the minimum of the axial N-index assignment problem by means of the set of plane stochastic tensors.
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content type line 14
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2018.1453469