Characteristic polynomials and controlability of partially prescribed matrices

In a previous paper it was proved that n-1 arbitrary entries and the charac teristic polynomial of an n x n matrix over a field F can be arbitrarily pr escribed, except if all the nonprincipal entries of a row or column are pre scribed equal to zero and the characteristic polynomial does not have a roo t in F. This paper describes the possible characteristic polynomials of a pk x pk m atrix, partitioned into k x k blocks of size p x p when k - 1 blocks are fi xed and the others vary. It also studies the possibility of a pair of matrices (A(1), A(2)), where A (1) is square and [A(1) A(2)] is partitioned into k x (k + 1) blocks of siz e p x p, being completely controllable when some of the blocks are prescrib ed and the others vary. (C) 2001 Elsevier Science Inc. All rights reserved.