Before revision: For linear square matrix eigenproblems, eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors . A complex moment plays the role of a filter and extracts eigencomponents of interest from random vectors or matrices.
After revision: For linear square matrix eigenproblems, eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors of a regular linear matrix pencil. The complex moment acts as a filter for extracting eigencomponents of interest from random vectors or matrices.