A note on “Constructing matrices with prescribed off-diagonal submatrix and invariant polynomials” Original Research Article

Let image be any field and let B a matrix of image. Zaballa found necessary and sufficient conditions for the existence of a matrix image with prescribed similarity class and such that A21=B. In an earlier paper [A. Borobia, R. Canogar, Constructing matrices with prescribed off-diagonal submatrix and invariant polynomials, Linear Algebra Appl. 424 (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.