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...

The solvability and the properties of solutions of nonhomogeneous and homogeneous vector integral equation f x g x ∫∞ 0 k x − t f t dt ∫0 −∞ T x − t f t dt, where K, T are n × n matrix valued functions, n ≥ 1, with nonnegative integrable elements, are considered in one semiconservative singular case, where the matrix A ∫∞ −∞ K x dx is stochastic one and the matrix B ∫∞ −∞ T x dx is substochasti...

We present a test for determining if a substochastic matrix is convergent. By establishing a duality between weakly chained diagonally dominant (w.c.d.d.) Lmatrices and convergent substochastic matrices, we show that this test can be trivially extended to determine whether a weakly diagonally dominant (w.d.d.) matrix is a nonsingular M-matrix. The test’s runtime is linear in the order of the in...

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...

We construct upper and lower bounds for Cheeger-type constants for transient Markov chains. We first treat the situation where there is a detailed balance condition and obtain bounds that rely exclusively on the first and second eigenvalues of the substochastic transition matrix. Secondly, we consider general substochastic transition matrices and develop bounds in this broader setting. The effi...

Some special subsets of the set of uniformly tapered doubly stochastic matrices are considered. It is proved that each such subset is a convex polytope and its extreme points are determined. A minimality result for the whole set of uniformly tapered doubly stochastic matrices is also given. It is well known that if x and y are nonnegative vectors of R and x is weakly majorized by y, there exist...

By elementary linear algebra involving row operations (replacing row i by row i plus row j), and column exchanges, we can write G as (Ik|A) where A is some k×n−k matrix. Now the matrix H = ( −A In−k ) satisfies GH = 0. Thus every vector y = xG satisfies yH = 0. Furthermore standard linear algebra implies that the space of vectors that satisfies yH = 0 is at most k and so this must be the space ...

2 This paper considers the subexponential asymptotics of the stationary distributions of GI/G/1-type Markov chains in two cases: (i) the phase transition matrix in non-boundary levels is stochastic; and (ii) it is strictly substochastic. For the case (i), we present a weaker sufficient condition for the subexponential asymptotics than those given in the literature. As for the case (ii), the sub...