相关论文: A new S-type eigenvalue localization set for tenso…
An S-type eigenvalue localization set for a tensor is given by breaking N={1,2,...,n} into disjoint subsets S and its complement. It is shown that the new set is tighter than those provided by L. Qi (Journal of Symbolic Computation 40…
A new $Z$-eigenvalue localization set for tensors is given and proved to be tighter than those presented by Wang \emph{et al}. (Discrete and Continuous Dynamical Systems Series B 22(1): 187-198, 2017) and Zhao (J. Inequal. Appl., to appear,…
A new $Z$-eigenvalue inclusion theorem for tensors is given and proved to be tighter than those in [G. Wang, G.L. Zhou, L. Caccetta, $Z$-eigenvalue inclusion theorems for tensors, Discrete and Continuous Dynamical Systems Series B,22(1)…
A new S-type singular value inclusion set for rectangular tensors is given and proved to be tighter than that in [Sang C.L., An S-type singular value inclusion set for rectangular tensors, J. Inequal. Appl. 2017: 141, 2017]. Based on this…
We introduce $\hat{H}$-eigenvalue for $2m$-th order $n$-dimensional complex tensors. Then we determine several checkable inclusion sets for $\hat{H}$-eigenvalues and derive some criterions for the Hermitian positive definiteness…
By excluding some sets, which don't include any eigenvalue of a tensor, from some existing eigenvalue inclusion sets, two new sets are given to locate all eigenvalues of a tensor. And it is shown that these two sets are contained in the…
This article introduces an algebraic framework for establishing eigenvalue bounds for symmetric positive definite tensors by leveraging intrinsic invariants, specifically the trace and determinant (resultant). We derive a hierarchy of…
We first prove two new spectral properties for symmetric nonnegative tensors. We prove a maximum property for the largest H-eigenvalue of a symmetric nonnegative tensor, and establish some bounds for this eigenvalue via row sums of that…
In this paper, one of our main purposes is to prove the boundedness of solution set of tensor complementarity problem with B tensor such that the specific bounds only depend on the structural properties of tensor. To achieve this purpose,…
In this paper, we give a further study on $B$-tensors and introduce doubly $B$-tensors that contain $B$-tensors. We show that they have similar properties, including their decompositions and strong relationship with strictly (doubly)…
In this paper, a new class of positive semi-definite tensors, the MO tensor, is introduced. It is inspired by the structure of Moler matrix, a class of test matrices. Then we focus on two special cases in the MO-tensors: Sup-MO tensor and…
Finding the maximum eigenvalue of a symmetric tensor is an important topic in tensor computation and numerical multilinear algebra. This paper is devoted to a semi-definite program algorithm for computing the maximum $H$-eigenvalue of a…
In this article, we define new classes of tensors called double $\overline{B}$-tensors, quasi-double $\overline{B}$-tensors and establish some of their properties. Using these properties, we construct new regions viz., double…
In this paper, we prove that all H$^+$(Z$^+$)-eigenvalues of each principal sub-tensor of a strictly semi-positive tensor are positive. We define two new constants associated with H$^+$(Z$^+$)eigenvalues of a strictly semi-positive tensor.…
This paper addresses two fundamental problems posed by Qi regarding the sufficiency of eigenvalues for the classification of symmetric tensors in the two-dimensional setting. For $2\times2\times2$ and $2\times2\times2\times2$ complex…
In this paper, we introduce almost (strictly) semi-positive tensors, which extend the concept of almost (strictly) semimonotone matrices. Furthermore, we provide insights into the characteristics of the entries within these almost…
A tensor $\mathcal T\in \mathbb T(\mathbb C^n,m+1)$, the space of tensors of order $m+1$ and dimension $n$ with complex entries, has $nm^{n-1}$ eigenvalues (counted with algebraic multiplicities). The inverse eigenvalue problem for tensors…
The tensor complementarity problem is a specially structured nonlinear complementarity problem, then it has its particular and nice properties other than ones of the classical nonlinear complementarity problem. In this paper, it is proved…
Let $n$ be a positive integer and $m$ be a positive even integer. Let ${\mathcal A}$ be an $m^{th}$ order $n$-dimensional real weakly symmetric tensor and ${\mathcal B}$ be a real weakly symmetric positive definite tensor of the same size.…
In this paper, we give the Minc-type bound for spectral radius of nonnegative tensors. We also present the bounds for the spectral radius and the eigenvalue inclusion sets of the general product of tensors.