The maximal correlation problem (MCP) aiming at optimizing correlation between sets of variables plays a very important role in many areas of statistical applications. Currently, algorithms for the general MCP stop at solutions of the multivariate eigenvalue problem (MEP) for a related matrix A. The MEP is a necessary condition for the global solutions of the MCP. Up to date, there is no algori...

For a nonnegative n× n matrix A, we find that there is a polynomial f(x) ∈ R[x] such that f(A) is a positive matrix of rank one if and only if A is irreducible. Furthermore, we show that the lowest degree such polynomial f(x) with tr f(A) = n is unique. Thus, generalizing the well-known definition of the Hoffman polynomial of a strongly connected regular digraph, for any irreducible nonnegative...

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 ...

Let A be an n × n nonnegative matrix. In this paper we consider the problems of maximizing the spectral radii of (i) A + X and (ii) A + D, where X is a real n × n matrix whose Frobenius norm is restricted to be 1 and where D is as X but is further constrained to be a diagonal matrix. For both problems the maximums occur at nonnegative X and D, and we use tools of nonnegative matrices, most nota...

The concept of the Perron complement of a nonnegative and irreducible matrix was introduced by Meyer in 1989 and it was used to construct an algorithm for computing the stationary distribution vector for Markov chains. Here properties of the generalized Perron complement of an n×n irreducible Z-matrixK are considered. First the result that the generalized Perron complements of K are irreducible...

We consider the algebraic Riccati equation for which the four coefficient matrices form an M -matrix K. When K is a nonsingular M -matrix or an irreducible singular M -matrix, the Riccati equation is known to have a minimal nonnegative solution and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where K is a reducible singular M ...

The concept of the Perron complement of a nonnegative and irreducible matrix was introduced by Meyer in 1989 and it was used to construct an algorithm for computing the stationary distribution vector for Markov chains. Here properties of the generalized Perron complement of an n×n irreducible Z-matrixK are considered. First the result that the generalized Perron complements of K are irreducible...