Rank-one corrections of nonnegative matrices, with an application to matrix population models
The authors study the location of the second largest eigenvalue of a nonnegative matrix and what occurs with such a number under rank-one corrections. The main result proves that if a matrix \(B\) is a rank-one correction of a matrix \(A\) (both nonnegative), then \(B\) has at most one real eigenvalue (which is simple) greater than the leading eigenvalue of \(A\). It is shown that the analogue of such result is not true for eigenvalue modulus or for the eigenvalue real parts. Such results are applicable to matrix population models where the location of the second largest positive eigenvalue plays a crucial role.
scientific article; zbMATH DE number 6356195
scientific article