Eigenvalues and eigenvectors for matrices over distributive lattices Original Research Article

Let (L, less-than-or-equals, slant, logical and, logical or) be a complete and completely distributive lattice. A vector ξ is said to be an eigenvector of a square matrix A over the lattice L if Aξ = γξ for some γεL. The elements γ are called the associated eigenvalues. In this paper we characterize the eigenvalues and the eigenvectors and also the roots of the characteristic equation of A.