Abstract :
The integer m × n matrices A = (aij), B = (bij) are said to be equivalent if aij = ui + bij + vj for all i = 1,…,m,j = 1,…,n, for some u1,…,um,v1,…,vn set membership, variant Z. For an integer matrix X the symbol S(X) denotes the set of all nonnegative integer matrices equivalent to X having a zero element in each row and each column. We develop algorithms to solve the problems of the following type for a given class S(X) : decide whether A set membership, variant S(X); find the largest possible value for each position among all matrices in S(X); find a matrix in S(X) with prescribed values of a specified entry or row (column); find a matrix in S(X) with term rank 2. A complete description of those S(X) containing only zero-one matrices is presented.
