Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …

Tensors, as geometric objects that describe linear or multi-linear relations between
geometric vectors, scalars, and other tensors, have provided a concise mathematical …

Recent work by Kilmer and Martin [Linear Algebra Appl., 435 (2011), pp. 641--658] and
Braman [Linear Algebra Appl., 433 (2010), pp. 1241--1253] provides a setting in which the …

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 …

Further Results for Perron–Frobenius Theorem for Nonnegative Tensors Page 1 Copyright © by
SIAM. Unauthorized reproduction of this article is prohibited. SIAM J. MATRIX ANAL. APPL. c …

Recent work on eigenvalues and eigenvectors for tensors of order m≥3 has been motivated
by applications in blind source separation, magnetic resonance imaging, molecular …

We introduce M-tensors. This concept extends the concept of M-matrices. We denote Z-
tensors as the tensors with nonpositive off-diagonal entries. We show that M-tensors must be …

This paper is concerned with solving some structured multi-linear systems, especially
focusing on the equations whose coefficient tensors are M M-tensors, or called M M …

We prove an analog of Perron–Frobenius theorem for multilinear forms with nonnegative
coefficients, and more generally, for polynomial maps with nonnegative coefficients. We …

We study a general product of two n-dimensional tensors A and B with orders m⩾ 2 and k⩾
1. This product satisfies the associative law, and is a generalization of the usual matrix …