Row and column orthogonal (0,1)-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.

Row and Column Distributions of Letter Matrices

A letter matrix is an n-by-n matrix whose entries are n symbols, each appearing n times. The row (column) distribution of a letter matrix is an n-by-n nonnegative integer matrix that tells how many of each letter are in each row (column). A row distribution R and a column distribution C are compatible if there exits a letter matrix A whose row distribution is R and whose column distribution is ...

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

Row and Column Spaces of Matrices over Residuated Lattices

We present results regarding row and column spaces of matrices whose entries are elements of residuated lattices. In particular, we define the notions of a row and column space for matrices over residuated lattices, provide connections to concept lattices and other structures associated to such matrices, and show several properties of the row and column spaces, including properties that relate ...