International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 37580, 11 pages
doi:10.1155/2007/37580
Research Article
Determinant and Inverse of Meet and Join Matrices
1Department of Mathematics, Faculty of Arts and Sciences, Gazi University, Teknikokullar 06500, Ankara, Turkey
2Department of Mathematics, Statistics and Philosophy, University of Tampere, Tampere 33014, Finland
Received 2 March 2007; Accepted 18 April 2007
Academic Editor: Dihua Jiang
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.
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.