EIGENVALUES AND EIGENVECTORS FOR MATRICES OVER DISTRIBUTIVE LATTICES

Let(L, less than or equal to, boolean OR, boolean AND) be a complete a nd completely distributive lattice. A vector xi is said to be an eigen vector of a square matrix A over the lattice L if A xi = lambda xi for some lambda is an element of L. The elements lambda are called the as sociated eigenvalues. In this paper we characterize the eigenvalues an d the eigenvectors and also the roots of the characteristic equation o f A. (C) 1998 Elsevier Science Inc. All rights reserved.