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 arbit rary field. We describe the possible characteristic polynomials of [A B], w hen some of its rows are prescribed and the other rows vary. The characteri stic polynomial of [A B] is defined as the largest determinantal divisor (o r the product of the invariant factors) of [xI(n) - A - B]. This result gen eralizes 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.