Possible line sums for a qualitative matrix

Given m-ordered row sums r(1),..., r(m) and n-ordered column sums c(1),..., c(n), we characterize the sign patterns for which there is a real m-by-n m atrix B with row sums r(1),..., r(m) and column sums c(1),..., c(n). Situat ions in which there is a symmetric solution or in which there is a skew-sym metric solution are characterized, and circumstances in which there is a so lution when +'s or -'s are relaxed to 0 are also determined. Most generally , our principal result may be used to characterize those sign patterns for which for given vectors x, v is an element of R-n and y, u is an element of R-m there is a real m-by-n matrix B such that Bx = y and v(T) = u(T)B. (C) 2001 Elsevier Science Inc. All rights reserved.