Determinant and Inverse of Meet and Join Matrices

Altinisik, Ercan; Tuglu, Naim; Haukkanen, Pentti

doi:https://doi.org/10.1155/2007/37580

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 037580 | https://doi.org/10.1155/2007/37580

Determinant and Inverse of Meet and Join Matrices

Ercan Altinisik,¹Naim Tuglu,¹and Pentti Haukkanen²

Academic Editor: Dihua Jiang

Received02 Mar 2007

Accepted18 Apr 2007

Published21 May 2007

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.

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Copyright

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.

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