Article ID Journal Published Year Pages File Type
4602375 Linear Algebra and its Applications 2008 11 Pages PDF
Abstract

A connection is established between the problem of characterizing all possible real spectra of entrywise nonnegative matrices (the so-called real nonnegative inverse eigenvalue problem) and a combinatorial process consisting in repeated application of three basic manipulations on sets of real numbers. Given realizable sets (i.e., sets which are spectra of some nonnegative matrix), each of these three elementary transformations constructs a new realizable set. This defines a special kind of realizability, called C-realizability and this is closely related to the idea of compensation. After observing that the set of all C-realizable sets is a strict subset of the set of realizable ones, we show that it strictly includes, in particular, all sets satisfying several previously known sufficient realizability conditions in the literature. Furthermore, the proofs of these conditions become much simpler when approached from this new point of view.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory