International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 37580, 11 pages
doi:10.1155/2007/37580
Determinant and inverse of meet and join matrices
Ercan Altinisik1
, Naim Tuglu1
and Pentti Haukkanen3
1Department of Mathematics, Faculty of Arts and Sciences, Gazi University, Teknikokullar 06500, Ankara, Turkey
3Department of Mathematics, Statistics and Philosophy, University of Tampere, Tampere 33014, Finland
Abstract
We define meet and join matrices on two subsets X and Y of a lattice (P,≼) with respect 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.