Radicals with integrity and row-finite matrices

Matrices with Prescribed Row and Column Sums

This is a survey of the recent progress and open questions on the structure of the sets of 0-1 and non-negative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from the set, discrete versions of the Brunn-Minkowski inequality and the statistical dependence between row and column sums.

Estimation of matrices with row sparsity

An increasing number of applications is concerned with recovering a sparsity can be defined in terms of lq balls for q 2 [0, 2), defined as Bq(s) = { v = (vi) 2 R2 : n2 ∑

Row Products of Random Matrices

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 ...

Integral Matrices with Given Row and Column Sums

Let P = (p,,) and Q = (qij) be m x n integral matrices, R and S be integral vectors. Let Nf(R, S) denote the class of all m x n integral matrices A with row sum vector R and column sum vector S satisfying P < A < Q. For a wide variety of classes ‘%$I( R, S) satisfying our main condition, we obtain two necessary and sufficient conditions for the existence of a matrix in @(R, 5). The first charac...

On nonnegative matrices with given row and column sums