doi:10.1155/2007/37580 Research Article Determinant and Inverse of Meet and Join Matrices

We define meet and join matrices on two subsets X and Y of a lattice (P, ) with re-spect to a complex-valued function f on P by (X,Y) f = ( f (xi ∧ yi)) and [X,Y] f = ( f (xi ∨ yi)), respectively. We present expressions for the determinant and the inverse of (X,Y) f and [X,Y] f, and as special cases we obtain several new and known formulas for the determinant and the inverse of the usual meet and join matrices (S) f and [S] f. Copyright © 2007 Ercan Altinisik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1