NDLI: ℋ-tensors and nonsingular ℋ-tensors

Content Provider	Springer Nature Link
Author	Wang, Xuezhong Wei, Yimin
Copyright Year	2016
Abstract	The H-matrices are an important class in the matrix theory, and have many applications. Recently, this concept has been extended to higher order ℋ-tensors. In this paper, we establish important properties of diagonally dominant tensors and ℋ-tensors. Distributions of eigenvalues of nonsingular symmetric ℋ-tensors are given. An ℋ$_{+}$-tensor is semi-positive, which enlarges the area of semi-positive tensor from M-tensor to ℋ$_{+}$-tensor. The spectral radius of Jacobi tensor of a nonsingular (resp. singular) ℋ-tensor is less than (resp. equal to) one. In particular, we show that a quasi-diagonally dominant tensor is a nonsingular ℋ-tensor if and only if all of its principal sub-tensors are nonsingular ℋ-tensors. An irreducible tensor A is an ℋ-tensor if and only if it is quasi-diagonally dominant.
Starting Page	557
Ending Page	575
Page Count	19
File Format	PDF
ISSN	16733452
Journal	Frontiers of Mathematics in China
Volume Number	11
Issue Number	3
e-ISSN	16733576
Language	English
Publisher	Higher Education Press
Publisher Date	2015-09-02
Publisher Institution	Chinese Universities
Publisher Place	Beijing
Access Restriction	Subscribed
Subject Keyword	Diagonally dominant irreducible diagonally dominant ℋ-tensor nonsingular Eigenvalues, singular values, and eigenvectors Multilinear algebra, tensor products Eigenvalues, eigenvectors Iterative methods for linear systems Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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