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On the Multiplicative Inverse Eigenvalue Problem

Published online by Cambridge University Press:  12 February 2019

G. N. De Oliveira
G. N. De Oliveira*
Affiliation:
Instituto Gulbenkian De Ciência, C.C.C., Oeiras, Portugal
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 189 - 194
Copyright
Copyright © Canadian Mathematical Society 1972

References

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