Let　(L,　≤,　∨,　∧)　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　=　λξ　for　some　λ　∈　L.　The　elements　λ　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.　©　1998　Elsevier　Science　Inc.　All　rights　reserved.