On the characteristic polynomial of matrices with prescribed rows

Let A is an element of F-nxn, B is an element of F-nxt, where F is an arbitrary field. We describe the possible characteristic polynomials of [A B], when some of its rows are prescribed and the other rows vary. The characteristic polynomial of [A B] is defined as the largest determinantal divisor (or the product of the invariant factors) of [xI(n) - A - B]. This result generalizes a previous theorem by H. Wimmer [Monasth. Math. 78 (1974) 256-263], which studies the same problem when t = 0. (C) 1999 Elsevier Science Inc. All rights reserved.