Abstract

The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and sufficient conditions for a list of complex numbers ¦O to be the spectrum of a nonnegative matrix. In this paper the problem is completely solved in the case when all numbers in the given list except for one (the Perron eigenvalue) are pure image numbers. Lets. Let ( ,bi, bi,,b i, b i)be a list of complex numbers with ¦N,bj > 0 for j =1,2,,k . A simple necessary and sufficient conditions for the existence of an entry wise nonnegative 2k +1 order matrix A with spectrum ¦O are presented , and the proof is elementary.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.