In this paper we generalize (finite) block diagonal matrices to infinite dimensions and then by using row stochastic (as a special case), define the relation < bdr on c0, which is said majorization. We also obtain some important properties of Pbdr, set all bounded linear operators T : c0 ? c0; preserve Further, it obtained necessary conditions for operator be preserver majorization bdr. Also...

In this paper we show how to construct diagonal scalings for arbitrary matrix pencils $\lambda B-A$, in which both $A$ and $B$ are complex matrices (square or nonsquare). The goal of such is “balance” some sense the row column norms pencil. We see that problem scaling a pencil equivalent sums particular nonnegative matrix. However, it known there exist square nonsquare cannot be scaled arbitrar...

An alternating sign matrix is a square matrix with entries 1, 0 and −1 such that the sum of the entries in each row and each column is equal to 1 and the nonzero entries alternate in sign along each row and each column. To some of the symmetry classes of alternating sign matrices and their variations, G. Kuperberg associate square ice models with appropriate boundary conditions, and give determ...

The completely positive operators, which can be viewed as a generalization of the nonnegative matrices, are maps between spaces of linear operators arising in the study of C*-algebras. The existence of the operator analogues of doubly stochastic scalings of matrices is equivalent to a multitude of problems in computer science and mathematics, such rational identity testing in non-commuting vari...

Let ∆1, . . . ,∆K be d × n matrices. We define the row product of these matrices as a d × n matrix, whose rows are entry-wise products of rows of ∆1, . . . ,∆K . This construction arises in certain computer science problems. We study the question, to which extent the spectral and geometric properties of the row product of independent random matrices resemble those properties for a d × n matrix ...

Abstract Solution appraisal, which has been realized on the basis of projections from true medium to solution, is an essential procedure in practical studies, especially computer tomography. The projection operator a linear problem or its approximation nonlinear resolution matrix for solution (or model). Practical applications can be used quantitatively retrieve resolvability medium, constraina...

This work deals with the generalized eigenvalue problem for nonsquare matrix pencils A − λB such that matrices A,B ∈ MC (m×n) show a given structure. More precisely, we assume they result from removing the first row of some matrix G ∈ MC ((m+1) , n) in the case of A, and its last row in the case of B. This structured generalized eigenvalue problem can be found in signal processing methods and i...