On the eigenproblem of matrices over distributive lattices. (Q1414154)

The author considers the eigenproblem for matrices over the class of complete and completely distributive lattices. He obtains the eigenvector of a given matrix \(A\) for a given eigenvalue \(l\), and gives some properties of the maximum matrix \(M(l,x)\) in \(T(l,x)\), the set of matrices with given eigenvector \(x\) and eigenvalue \(l\). Then he introduces the concept of primitive vectors and considers the structure of matrices which possess a given primitive eigenvector \(x\) and shows in particular that, for any given \(l \) in \(L\), there is a matrix, namely \(M(l,x)\), having \(x\) as a maximal primitive eigenvector associated with the eigenvalue \(l\).