Open AccessEigenset generalizations of the eigenvalue concept
Author(s) -
Charles R. Johnson
Publication year - 1977
Publication title -
journal of research of the national bureau of standards
Language(s) - English
Resource type - Journals
eISSN - 2376-5259
pISSN - 0160-1741
DOI - 10.6028/jres.082.013
Subject(s) - eigenvalues and eigenvectors , mathematics , calculus (dental) , pure mathematics , physics , medicine , quantum mechanics , dentistry
For an n-by-n complex matrix A some generalizations of the eigenvalue-eigenvector equation A x = λ x , 0 ≠ x ∈ C nare investigated. These take the form A S = λ S or A S ⊆ λ S where S is a suhset of C n about which various assumptions are made. For example, it is shown that there exists a finite set S ⊂ C n , the sum of whose elements is not 0, such that AS = λS , if and only if λ is an eigenvalue of A in the usual sense. The requirement that the sum of the elements of S is not 0 should he viewed as a natural analog of the requirement x ≠ 0 in the classical eigenvalue-eigenvector equation.