On the Multiplicative Inverse Eigenvalue Problem

Abstract

By "multiplicative inverse eigenvalue problem" (m.i.e.p., for short) we mean the following. Let A be an n×n matrix and let s1,…, sn be n given numbers. Under what conditions does there exist an n×n diagonal matrix V such that VA has eigenvalues s1,…,sn?In the "additive inverse eigenvalue problem" (a.i.e.p., for short) we seek the diagonal matrix V so that A + V has eigenvalues s1,…, sn?.In the present paper we extend to the m.i.e.p. the ideas used in [7] for the a.i.e.p.By per X we denote the permanent of the square matrix X.