A unified view on compensation criteria in the real nonnegative inverse eigenvalue problem (Q924330)

The authors establish a connection between the 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, 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, it is shown that it strictly includes, in particular, all sets satisfying several previously known sufficient realizability conditions.