Matrices with prescribed eigenvalues and prescribed submatrices II

Abstract

Let F be a field and let n, p1, p2, p3 be positive integers such that n= p1+ p2+ p3. LetC=C1 1C1 2C1 ,3C2 ,1C2 ,2C2 ,3C3 ,1C3 ,2C3 ,3∈Fn× n,where the blocks Ci, j∈F pi×pj,i,j∈{1,2,3}. In this paper we describe the eigenvalues of C, when C1 ,2,C1 ,3, C2 ,2 are prescribed (with C1 ,3=0) and the other blocks are unknown. For the same prescription of blocks (for arbitrary prescription of C1 ,3), we still provide a sufficient condition for the prescription of the characteristic polynomial of C. © 2011 Elsevier Inc. All rights reserved.