A parallel algorithm is presented for computing the group inverse of a singular M–matrix of the form A = I − T , where T ∈ Rn×n is irreducible and stochastic. The algorithm is constructed in the spirit of Meyer’s Perron complementation approach to computing the Perron vector of an irreducible nonnegative matrix. The asymptotic number of multiplication operations that is necessary to implement t...

We relate some minimax functions of matrices to some spectral functions of matrices. If A is a nonnegative n X n matrix, v(A) is the gametheoretic value of A, and p(A) is the spectral radius of A, then v(A) < p(A). Necessary and sufficient conditions for v(A) = p(A) are given. It follows that if A is nonnegative and irreducible and n > 1, then v(A) < p(A). Also, if, for a real matrix A and a po...

A parallel algorithm is presented for computing the group inverse of a singular M–matrix of the form A = I − T , where T ∈ Rn×n is irreducible and stochastic. The algorithm is constructed in the spirit of Meyer’s Perron complementation approach to computing the Perron vector of an irreducible nonnegative matrix. The asymptotic number of multiplication operations that is necessary to implement t...

In [l] R. Sinkhorn proved the following theorem: Let A be a positive square matrix. Then there exist two diagonal matrices D, , D, whose diagonal elements are positive such that D,AD, is doubly stochastic. Moreover, these matrices are uniquely determkd up to scalar factors. In addition, Sinkhorn gave some examples which show that the theorem fails for some nonnegative matrices A. Marcus and New...

this paper presents a modified digital image watermarking method based on nonnegative matrix factorization. firstly, host image is factorized to the product of three nonnegative matrices. then, the centric matrix is transferred to discrete cosine transform domain. watermark is embedded in low frequency band of this matrix and next, the reverse of the transform is computed. finally, watermarked ...

This paper presents a modified digital image watermarking method based on nonnegative matrix factorization. Firstly, host image is factorized to the product of three nonnegative matrices. Then, the centric matrix is transferred to discrete cosine transform domain. Watermark is embedded in low frequency band of this matrix and next, the reverse of the transform is computed. Finally, watermarked ...

Our proof is built on Perron-Frobenius theorem, a seminal work in matrix theory (Meyer 2000). By Perron-Frobenius theorem, the power iteration algorithm for predicting top K persuaders converges to a unique C and this convergence is independent of the initialization of C if the persuasion probability matrix P is nonnegative, irreducible, and aperiodic (Heath 2002). We first show that P is nonne...

Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible...

This note presents a new proof of basic Perron{Frobenius theory of irreducible nonnegative matrices. ABSTRACT This note presents a new proof of basic Perron{Frobenius theory of irreducible nonnegative matrices.

In this paper, we give some new sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. Using these bounds, we obtain some new and improved bounds for the signless Laplacian spectral radius of a graph or a digraph.