On pairs of multidimensional matrices (Q1059694)

Recently \textit{R. Bapat} [ibid. 48, 437-442 (1982; Zbl 0503.15008)] applied a topological theorem of Kronecker and generalized a theorem of Sinkhorn on positive matrices. Here we give an alternative proof of a slightly stronger version of his generalization. This proof combines Kakutani's fixed point theorem and the duality theorem of linear programming and gives yet another proof of a theorem of Bacharach and Menon on pairs of nonnegative matrices.