for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

for vectors x, y ∈ rn, it is said that x is left matrix majorizedby y if for some row stochastic matrix r; x = ry. the relationx ∼` y, is defined as follows: x ∼` y if and only if x is leftmatrix majorized by y and y is left matrix majorized by x. alinear operator t : rp → rn is said to be a linear preserver ofa given relation ≺ if x ≺ y on rp implies that t x ≺ ty onrn. the linear preservers o...

in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.

in this paper, at rst for a given set of real or complex numbers  with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which  is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.

A new method for feature extraction and recognition, namely the fuzzy bidirectional weighted sum criterion (FBWSC) is proposed in this paper. FBWSC defines the row directional fuzzy image optimal image projection matrix. Subsequently, each sample in the original training sample set is transformed using the row directional optimal image projection matrix, and the row directional feature training...

Given a distance matrix M that specifies the pairwise evolutionary distances between n species, the phylogenetic tree reconstruction problem asks for an edge-weighted phylogenetic tree that satisfies M, if one exists. We study some extensions of this problem to rooted phylogenetic networks. Our main result is an O(n(2) log n)-time algorithm for determining whether there is an ultrametric galled...

The problem of the optimal assignment of facilities to locaticns has been solved by J. W. Gavett and Normann V. PlyterD• In their paper the branch and bound technique2) is used and for this purpose the distance matrix is transformed into the matrix whose diagonal compoents are zero. The purpose of this paper is to avoid such a transformation and the store of the distance matrix into the computer.

This paper examines cluster consensus for multi-agent systems on matrix-weighted switching networks. Necessary and/or sufficient conditions under which can be achieved are obtained, as well quantitative characterization of the steady-state consensus. Specifically, when underlying network switches amongst a finite number networks, necessary condition networks is derived; moreover, it shown that ...