Perron-Frobenius theorem for nonnegative tensors

By Kung-Ching Chang, Kelly J. Pearson, Tan Zhang. 2008

557 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/383cbad473d20424ff281db73688b8de794db08a

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In Computational Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Singular values of a real rectangular tensor (2010, methodology): “as the Perron-Frobenius theorem for eigenvalues of nonnegative square tensors [2] have been established.”
On the spectrum of hypergraphs (2017, background): “Various properties of eigenvalues of a tensor have been studied in [10, 11, 24, 31, 41, 42, 45, 46].”
An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors (2016, background): “[1,4,5] Eigenvalue problems of tensors have become an important topic of study in numerical multilinear algebra, and they have a wide range of practical applications; see, [5–30].”
M-Tensors and Some Applications (2014, unknown): “In particular, theory of, and algorithms for calculating, eigenvalues of nonnegative tensors are well developed [6, 7, 8, 12, 16, 18, 19, 23, 26, 27, 28].”
Z-tensors and complementarity problems (2015, background): “Properties of nonnegative tensors, particularly in relation to the Perron-Frobenius theorem, have been explored in several recent papers, see [3, 24, 23, 26].”
A new eigenvalue inclusion set for tensors and its applications (2015, background): “Recently, tensor eigenvalues and eigenvectors have received much attention in the literature [1,8,9,11,15,18–22,25].”
The largest Laplacian and signless Laplacian H-eigenvalues of a uniform hypergraph (2013, background): “The largest signless Laplacian H-eigenvalue is the spectral radius of the signless Laplacian tensor [3,18,23], since the signless Laplacian tensor is a nonnegative tensor.”
Connected Hypergraphs with Small Spectral Radius (2014, unknown): “[2, 5, 10, 17] Given an r-uniform hypergraph H, the polynomial form of H is a function PH(x) : R n → R defined for any vector x := (x1, .”
Conditions for strong ellipticity and M-eigenvalues (2009, background): “is its relation with M-eigenvalues here? Chang, Pearson and Zhang [2] established the Perron-Frobenius theorem for nonnegative tensors.”
An S-type eigenvalue localization set for tensors (2015, background): “Let A = (aijkl) ∈ R [4,3] be a real symmetric tensor with elements defined as follows: a1111 = 5, a2222 = 6, a3333 = 3.”
On the limiting probability distribution of a transition probability tensor (2014, background): “[17] gave a specific condition to show the uniqueness of positive Z -eigenvector.”
Nonsingular $H$-tensor and its criteria (2016, methodology): “We first present some definitions developed in tensor analysis [2, 20, 28] and then introduce some kinds of specially structured tensors.”