Let A∈Rn×n be an irreducible totally nonnegative matrix with rank r and principal p, that is, all minors of A are nonnegative, is the size largest invertible square submatrix p its submatrix. triple (n,r,p) called realizable if there exists n×n p. In this work we present a method to construct matrices associated prescribed Jordan canonical form corresponding zero eigenvalue.

in this paper for a given prescribed ritz values that satisfy in the some special conditions, we nd a symmetric nonnegative matrix, such that the given set be its ritz values.

Inequalities for convex functions on the lattice of partitions of a set partially ordered by refinement lead to multivariate generalizations of inequalities of Cauchy and Rogers-Hölder and to eigenvalue inequalities needed in the theory of population dynamics in Markovian environments: If A is an n× n nonnegative matrix, n > 1, D is an n× n diagonal matrix with positive diagonal elements, r(·) ...

Utilizing the concept of Perron complement, a new estimate for the spectral radius of a nonnegative irreducible matrix is presented. A new matrix is derived that preserves the spectral radius while its minimum row sum increases and its maximum row sum decreases. Numerical examples are provided to illustrate the effectiveness of this approach.

Utilizing the concept of Perron complement, a new estimate for the spectral radius of a nonnegative irreducible matrix is presented. A new matrix is derived that preserves the spectral radius while its minimum row sum increases and its maximum row sum decreases. Numerical examples are provided to illustrate the effectiveness of this approach.

We offer an almost self-contained development of Perron–Frobenius type results for the numerical range of an (irreducible) nonnegative matrix, rederiving and completing the previous work of Issos, Nylen and Tam, and Tam and Yang on this topic. We solve the open problem of characterizing nonnegative matrices whose numerical ranges are regular convex polygons with center at the origin. Some relat...

The eigenvalue problem for an irreducible nonnegative matrix A = a ij ] in the max algebra system is A x = x, where (A x) i = max j (a ij x j) and turns out to be the maximum circuit geometric mean, (A). A power method algorithm is given to compute (A) and eigenvector x. This method generalizes and simpliies an algorithm due to Braker and Olsder. The algorithm is developed by using results on t...