Matrices with prescribed eigenvalues and prescribed submatrices II

Let F be a field and let n, p(1), p(2), p(3) be positive integers such that n = p(1) + p(2) + p(3). Let C = [GRAPHICS] is an element of F-nxn, where the blocks C-ij is an element of F-pixpj, i, j is an element of {1, 2, 3}. In this paper we describe the eigenvalues of C, when C-1,C-2, C-1,C-3, C-2,C-2 are prescribed (with C-1,C-3 = 0) and the other blocks are unknown. For the same prescription of blocks (for arbitrary prescription of C-1,C-3), we still provide a sufficient condition for the prescription of the characteristic polynomial of C. (c) 2012 Elsevier Inc. All rights reserved.