EXISTENCE OF MATRICES WITH PRESCRIBED OFF-DIAGONAL BLOCK ELEMENT MAXIMA

Necessary and sufficient conditions are proven for the existence of a real square matrix such that for every principal submatrix the maximal (or minimal) value of an element in the row complement of the submatr ix is prescribed. The problem is solved in the cases where the positio ns of the nonzero elements of A are contained in a given set of positi ons, where the positions of the nonzero elements of A are all given, a nd where there is no restriction on the positions of the nonzero eleme nts of A. The uniqueness of the solution is studied as well.