Studying new generalizations of Max-Min matrices with a novel approach

We consider new kinds of max and min matrices, [a(max(i, j))](i,j >= 1) and [a(min(i, j))](i,j >= 1), as generalizations of the classical max and min matrices. Moreover, their reciprocal analogues for a given sequence {a(n)} have been studied. We derive their LU and Cholesky decompositions and their inverse matrices as well as the LU-decompositions of their inverses. Some interesting corollaries will be presented.