Bounds and inequalities for the Perron root of a nonnegative matrix. III: Bounds dependent on simple paths and circuits.
Bounds for graph expansions via elasticity.
Bounds for the singular values of a matrix involving its sparsity pattern.
Bounds for the spectral radius of nonnegative matrices
Bounds for the Z-eigenpair of general nonnegative tensors
In this paper, we consider the Z-eigenpair of a tensor. A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented. Furthermore, upper bounds of Z-spectral radius of nonnegative tensors and general tensors are given. The proposed bounds improve some existing ones. Numerical examples are reported to show the effectiveness of the proposed bounds.
Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefinite matrices.
Bounds on the spectral radius of Hadamard products of positive operators on -spaces.
Bounds on the subdominant eigenvalue involving group inverses with applications to graphs
Let be an symmetric, irreducible, and nonnegative matrix whose eigenvalues are . In this paper we derive several lower and upper bounds, in particular on and , but also, indirectly, on . The bounds are in terms of the diagonal entries of the group generalized inverse, , of the singular and irreducible M-matrix . Our starting point is a spectral resolution for . We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity of undirected...
Brève communication. Sur la séparation des valeurs propres d'une matrice positive
Brèves communications. Un corollaire du théorème de Perron-Frobenius
Brownian motion tree models are toric
Felsenstein's classical model for Gaussian distributions on a phylogenetic tree is shown to be a toric variety in the space of concentration matrices. We present an exact semialgebraic characterization of this model, and we demonstrate how the toric structure leads to exact methods for maximum likelihood estimation. Our results also give new insights into the geometry of ultrametric matrices.