Let(L,　less　than　or　equal　to,　boolean　OR,　boolean　AND)　be　a　complete　and　completely　distributive　lattice.　A　vector　xi　is　said　to　be　an　eigenvector　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　associated　eigenvalues.　In　this　paper　we　characterize　the　eigenvalues　and　the　eigenvectors　and　also　the　roots　of　the　characteristic　equation　of　A.　(C)　1998　Elsevier　Science　Inc.　All　rights　reserved.