let a and b be n × m matrices. the matrix b is said to be g-row majorized (respectively g-column majorized) by a, if every row (respectively column) of b, is g-majorized by the corresponding row (respectively column) of a. in this paper all kinds of g-majorization are studied on mn,m, and the possible structure of their linear preservers will be found. also all linear operators t : mn,m ---> mn...

Suppose $textbf{M}_{n}$ is the vector space of all $n$-by-$n$ real matrices, and let $mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. A matrix $Rin textbf{M}_{n}$ is said to be $textit{row substochastic}$ if it has nonnegative entries and each row sum is at most $1$. For $x$, $y in mathbb{R}^{n}$, it is said that $x$ is $textit{sut-majorized}$ by $y$ (denoted by $ xprec_{sut} y$) if t...

Let D be a non empty set, let us consider k, and let M be a matrix over D. Then M k is a matrix over D. We now state four propositions: (3) For every finite sequence M such that lenM = n+1 holds len(M n+1) = n: (4) Let M be a matrix over D of dimension n+1 m and M1 be a matrix over D. Then (i) if n > 0; then widthM = width(M n+1); and (ii) if M1 = hM(n+1)i; then widthM = widthM1: (5) For every ...

ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...

The article discusses the matrices of the 1 n A , m n A , m N A forms, whose inversions are: tridiagonal matrix 1  n A (n dimension of the matrix), banded matrix m n A  (m the half-width band of the matrix) or block-tridiagonal matrix m N A  (N=n x m – full dimension of the block matrix; m the dimension of the blocks) and their relationships with the covariance matrices of measurements with ...