Infinite and finite dimensional Hilbert tensors
Yisheng Song,Liqun Qi +1 more
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TLDR
In this article, it was shown that for an m-order n-dimensional Hilbert tensor (hypermatrix) H ∞ = (H i 1 i 2 ⋯ i m ) the spectral radius is not larger than n m − 1 sin π n, and an upper bound of its E-spectral radius is n m 2 sin ρ n.About:
This article is published in Linear Algebra and its Applications.The article was published on 2014-06-15 and is currently open access. It has received 54 citations till now. The article focuses on the topics: Spectral radius.read more
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Properties of Some Classes of Structured Tensors
Yisheng Song,Liqun Qi +1 more
TL;DR: In this paper, the authors extend some classes of structured matrices to higher-order tensors and discuss their relationships with positive semi-definite tensors, and some other structured tensors.
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Tensor Complementarity Problem and Semi-positive Tensors
Yisheng Song,Liqun Qi +1 more
TL;DR: In this article, it was shown that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector.
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Properties of Some Classes of Structured Tensors
Yisheng Song,Liqun Qi +1 more
TL;DR: It is shown that every principal sub-tensor of such a structured Tensor is still a structured tensor in the same class, with a lower dimension, and the potential links of such structured tensors with optimization, nonlinear equations, non linear complementarity problems, variational inequalities and the non-negative tensor theory are discussed.
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Global Uniqueness and Solvability for Tensor Complementarity Problems
TL;DR: A class of related structured tensors is introduced and it is shown that the corresponding tensor complementarity problem has the property of global uniqueness and solvability.
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Properties of Solution set of Tensor Complementarity Problem
Yisheng Song,Gaohang Yu +1 more
TL;DR: In this article, it was shown that a tensor is an S-tensor if and only if the tensor complementarity problem is feasible, and each Q-Tensor is a S-Tensor.
References
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Eigenvalues of a real supersymmetric tensor
TL;DR: It is shown that eigenvalues are roots of a one-dimensional polynomial, and when the order of the tensor is even, E-eigenvaluesare roots of another one- dimensional polynomials associated with the symmetric hyperdeterminant.
Proceedings ArticleDOI
Singular values and eigenvalues of tensors: a variational approach
TL;DR: A theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigen values is proposed.
Journal ArticleDOI
Perron-Frobenius theorem for nonnegative tensors
TL;DR: In this paper, the Perron-Frobenius Theorem for nonnegative matrices was generalized to the class of nonnegative tensors, and the authors generalized it to nonnegative matrix classes.
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Further Results for Perron-Frobenius Theorem for Nonnegative Tensors II
Qingzhi Yang,Yuning Yang +1 more
TL;DR: The spectral radius of a nonnegative irreducible tensor with positive trace is proved to be the unique eigenvalue on the spectral circle and the minimax theorem for tensors is proved.
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Symmetric nonnegative tensors and copositive tensors
TL;DR: In this paper, it was shown that the largest H-eigenvalue of a symmetric nonnegative tensor has a positive H-vector and that the diagonal elements of a copositive tensor must be nonnegative, and if each sum of a diagonal element and all the negative off-diagonal elements in the same row of a real symmetric tensor is nonnegative.