Similar to the well known Schur Horn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a Hermitian matrix the Sing Thompson theorem characterizes the relationship between the diagonal en tries and the singular values of an arbitrary matrix It is noted in this paper that based on the induction principle such a matrix can be constructed numerically by...

We study the ramifications of Schur’s theorem that, if G is a group such that G/ZG is finite, then G′ is finite, if we restrict attention to nilpotent group. Here ZG is the center of G, and G′ is the commutator subgroup. We use localization methods and obtain relativized versions of the main theorems. 2000 Mathematics Subject Classification. 20B07, 20D15.

In this paper, we obtain a theorem on the distribution of eigenvalues for Schur complements of H-matrices. Further, we give some properties of diagonal-Schur complements on diagonally dominant matrices and their distribution of eigenvalues. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A45; 15A48

the main objective of this paper is to find the necessary and sufficient condition of a given finslermetric to be einstein in order to classify the einstein finsler metrics on a compact manifold. the consideredeinstein finsler metric in the study describes all different kinds of einstein metrics which are pointwiseprojective to the given one. this study has resulted in the following theorem tha...

Schur proved that for any finite partition of the naturals, some cell contains two numbers and their sum. We use Ramsey’s theorem to prove a noncommutative Schur theorem for permutation quadruples {x, y, xy, yx}. By Schur’s theorem [2], for any r ∈ N, there exists n ∈ N such that for any r-coloring of {1, 2, . . . , n}, one has a monochromatic “Schur triple.” That is, a 3-element set of the for...