On the Multiplicative Inverse Eigenvalue Problem
G. N. de Oliveira · Canadian Mathematical Bulletin · 1972
By "multiplicative inverse eigenvalue problem" (m.i.e.p., for short) we mean the following. Let A be an n×n matrix and let s 1 ,…, s n be n given numbers. Under what conditions does there exist an n × n diagonal matrix V such that VA has eigenvalues s 1 ,…, s n ? In the "additive inverse eigenvalue problem" (a.i.e.p., for short) we seek the diagonal matrix V so that A + V has eigenvalues s 1 ,…, s n ?. 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 .