Possible line sums for a qualitative matrix Original Research Article

Given m-ordered row sums r1,…,rm and n-ordered column sums c1,…,cn, we characterize the sign patterns for which there is a real m-by-n matrix B with row sums r1,…,rm and column sums c1,…,cn. Situations in which there is a symmetric solution or in which there is a skew-symmetric solution are characterized, and circumstances in which there is a solution when +ʹs or −ʹs 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, image and y, image there is a real m-by-n matrix B such that Bx=y and vT=uTB.