Constructive methods for spectra with three nonzero elements in the nonnegative inverse eigenvalue problem

Abstract

We present and compare three constructive methods for realizing nonreal spectra with three nonzero elements in the nonnegative inverse eigenvalue problem. We also provide some necessary conditions for realizability and numerical examples. In particular, we utilize the companion matrix.

Keywords:

• Nonnegative matrices
• inverse eigenvalue problem
• spectral theory

AMS Subject Classifications:

• 15A18
• 15A29
• 47A75
• 58C40

Acknowledgements

The author is very grateful for the hospitality he received at the Technion (under the Erasmus Mundus Action 2 EMAIL III mobility programme) during the completion of this paper and would like to sincerely thank Professor Tom Laffey and Professor Raphi Loewy for helpful conversations on this paper and ideas to improve its readability. Thanks also to the anonymous referee who gave this paper a very considered treatment and provided helpful comments.

Notes

No potential conflict of interest was reported by the author.