Determinant and Inverse of Meet and Join Matrices

Altinisik, Ercan; Tuglu, Naim; Haukkanen, Pentti (2007)
 
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Altinisik, Ercan
Tuglu, Naim
Haukkanen, Pentti
2007

International Journal of Mathematics and Mathematical Sciences 2007
37580
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doi:10.1155/2007/37580
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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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