A lower bound on the chromatic number of a graph is derived by majorization of spectra of weighted adjacency matrices. These matrices are given by Hadamard products of the adjacency matrix and arbitrary Hermitian matrices.

The information of interest is contained in the variance matrix, σ − = 2 1 V Q , or equivalently in the information matrix Q . The problem of finding estimators minimizing a decreasing convex functional of the variance matrix or maximizing an increasing concave functional of the information matrix is crucial in statistics. There are several optimality criteria in bibliography. We explain how th...

In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation. The effectiveness of the results are illustrated by numerical examples.

Let F and Fm be the usual spaces of n-dimensional column and m-dimensional row vectors on F, respectively, where F is the field of real or complex numbers. In this paper, the relations gsmajorization, lgw-majorization, and rgw-majorization are considered on F and Fm. Then linear maps T : F → F preserving lgw-majorization or gs-majorization and linear maps S : Fn → Fm, preserving rgw-majorizatio...

This paper tackles the problem of decomposing binary data using matrix factorization. We consider family mean-parametrized Bernoulli models, a class generative models that are well suited for modeling and enables interpretability factors. factorize parameter an additional Beta prior on one factors to further improve model's expressive power. While similar have been proposed in literature, they ...

We give a complete relation between the singular values and eigenvalues of a complex skew symmetric matrix in terms of multiplicative majorization and double occurrences of singular values and eigenvalues. Similar studies are given for matrices in the algebras spn(C) and spn(R).

There are important connections between majorization and convex polyhedra. Both weak majorization and majorization are preorders related to certain simple convex cones. We investigate the facial structure of a polyhedral cone C associated with a layered directed graph. A generalization of weak majorization based on C is introduced. It de nes a preorder of matrices. An application in statistical...

For many least-squares decomposition models efficient algorithms are well known. A more difficult problem arises in decomposition models where each residual is weighted by a nonnegative value. A special case is principal components analysis with missing data. Kiers (1997) discusses an algorithm for minimizing weighted decomposition models by iterative majorization. In this paper, we propose a m...