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...

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...

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...

2.1.1 matrix games A 2-player zero-sum game, or a matrix game, is defined by a matrix A ∈ Rm×n, called the payoff matrix. There are two players with opposing interests: the row player (minimizer) and the column player (maximizer). At each step of the play, the row player selects a row i, and the column player selects a column j, then the row player pays to the column player the value aij of the...

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 necessary condition for eigenvalue values of a circulant matrix is studied It is then proved that the necessary condition also su ces the existence of a circulant matrix with the prescribed eigenvalue values Introduction An n n matrix C of the form C c c cn cn c c cn cn cn c cn c c cn c is called a circulant matrix As each row of a circulant matrix is just the previous row cycled forward on...

We present an algorithm for computing a d-dimensional subspace of the row space of a matrix. For an n×n matrix A with m nonzero entries and with rank(A) ≥ d the algorithm generates a d × n matrix with full row rank and which is a subspace of Rows(A). If rank(A) < d the algorithm generates a rank(A)×n row-equivalent matrix. The running time of the algorithm is

Associated with any matrix, there are four fundamental subspaces: the column space, row space, (right) null space, and left null space. We describe a single computation that makes readily apparent bases for all four of these subspaces. Proofs of these results rely only on matrix algebra, not properties of dimension. A corollary is the equality of column rank and row rank. Bringing a matrix to r...

In this paper, we present a new sparse matrix data format that leads to improved memory coalescing and more efficient sparse matrix-vector multiplication (SpMV) for a wide range of problems on high throughput architectures such as a graphics processing unit (GPU). The sparse matrix structure is constructed by sorting the rows based on the row length (defined as the number of non-zero elements i...