Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773291 | Linear Algebra and its Applications | 2017 | 11 Pages |
Abstract
A list of complex numbers is realizable if it is the spectrum of a nonnegative matrix. In 1949 SuleıÌmanova posed the nonnegative inverse eigenvalue problem (NIEP): the problem of determining which lists of complex numbers are realizable. The version for reals of the NIEP (RNIEP) asks for realizable lists of real numbers. In the literature there are many sufficient conditions or criteria for lists of real numbers to be realizable. We will present an unified account of these criteria. Then we will see that the decision problem associated to the RNIEP is NP-hard and we will study the complexity for the decision problems associated to known criteria.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alberto Borobia, Roberto Canogar,