Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/11018
Title: M-tensors and nonsingular M-tensors
Authors: Ding, W
Qi, L 
Wei, Y
Keywords: Eigenvalues
H-tensors
M-tensors
Monotonicity
Nonsingular M-tensors
Semi-nonnegativity
Semi-positivity
Z-tensors
Issue Date: 2013
Publisher: North-Holland
Source: Linear algebra and its applications, 2013, v. 439, no. 10, p. 3264-3278 How to cite?
Journal: Linear algebra and its applications 
Abstract: The M-matrix is an important concept in matrix theory, and has many applications. Recently, this concept has been extended to higher order tensors [18]. In this paper, we establish some important properties of M-tensors and nonsingular M-tensors. An M-tensor is a Z-tensor. We show that a Z-tensor is a nonsingular M-tensor if and only if it is semi-positive. Thus, a nonsingular M-tensor has all positive diagonal entries; an M-tensor, regarding as the limit of a sequence of nonsingular M-tensors, has all nonnegative diagonal entries. We introduce even-order monotone tensors and present their spectral properties. In matrix theory, a Z-matrix is a nonsingular M-matrix if and only if it is monotone. This is no longer true in the case of higher order tensors. We show that an even-order monotone Z-tensor is an even-order nonsingular M-tensor, but not vice versa. An example of an even-order nontrivial monotone Z-tensor is also given.
URI: http://hdl.handle.net/10397/11018
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2013.08.038
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