On the distinguished eigenvalues of a cone-preserving map
Let A be a linear map which takes some proper cone K into itself. It is well known that the spectral radius of A is an eigenvalue and that there is a corresponding eigenvector in K. An eigenvalue of A is termed distinguished if there is a corresponding eigenvector in K. The author extends some results to the study of the Collatz-Wielandt sets which contain the distinguished eigenvalues. He then gives a cone theoretic proof for the existence of a nonnegative basis for the algebraic eigenspace of an (entrywise) nonnegative matrix. He then relates this to spectral properties of a map which preserves a polyhedral cone.
scientific article; zbMATH DE number 4146167
scientific article