A note on "Constructing matrices with prescribed off-diagonal submatrix and invariant polynomials"

Let F be any field and let B a matrix of F-qxp. Zaballa found necessary and sufficient conditions for the existence of a matrix A = [A(ij)](i,j) epsilon {1, 2} epsilon F(p+q)x(p+q) with prescribed similarity class and such that A(21) = B. In an earlier paper [A. Borobia, R. Canogar, Constructing matrices with prescribed off-diagonal submatrix and invariant polynomials, Linear Algebra Appl. 424 (2-3) (2007) 615-633] we obtained, for fields of characteristic different from 2, a finite step algorithm to construct A when it exists. In this short note we extend the algorithm to any field. (C) 2008 Elsevier Inc. All rights reserved.