Eigenset generalizations of the eigenvalue concept
Charles R. Johnson · Journal of Research of the National Bureau of Standards · 1977
For an n-by-n complex matrix A some ge neralizations of the eigenvalue-e ige nvector equation Ax = Ax, ° oF X € en are investigated .These take the formwhere S is a subset of en a bout whic h various assumptions a re made .For example, it is shown that the re ex ists a finite set See n, the sum of whose e le ments is not 0 , suc h that AS = AS , if and onl y if" is an eigenvalue of A in the usual sense.The require ment that the sum of the ele ments of S is not 0 should be viewed as a natural a nalog of the require ment x oF ° in the class ica l e igenvalue-e ige nvector equation.