Matrices with Prescribed Eigenvalues and Blocks, II

Abstract

Let F be a field and let n, p1, p2, p3 be positive integers such that n=p1+p2+p3. Let [Formula: see text] where the blocks Ci,j are of type pi× pj (i, j∈ {1,2,3}) and C1,1, C2,2, C3,3 are square submatrices. In this paper we describe conditions for which it is possible to prescribe arbitrarily the eigenvalues of C, when three arbitrary positions are prescribed and the remaining are free.