On the characteristic polynomial of matrices with prescribed rows Original Research Article

Let Aset membership, variantFn×n, Bset membership, variantFn×t, 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 [xIn−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.