Determinant and inverse of join matrices on two sets

Mathematics – Number Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

Let $(P,\preceq)$ be a lattice and $f$ a complex-valued function on $P$. We define meet and join matrices on two arbitrary subsets $X$ and $Y$ of $P$ by $(X,Y)_f=(f(x_i\wedge y_j))$ and $[X,Y]_f=(f(x_i\vee x_j))$ respectively. Here we present expressions for the determinant and the inverse of $[X,Y]_f$. Our main goal is to cover the case when $f$ is not semimultiplicative since the formulas presented earlier for $[X,Y]_f$ cannot be applied in this situation. In cases when $f$ is semimultiplicative we obtain several new and known formulas for the determinant and inverse of $(X,Y)_f$ and the usual meet and join matrices $(S)_f$ and $[S]_f$. We also apply these formulas to LCM, MAX, GCD and MIN matrices, which are special cases of join and meet matrices.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Determinant and inverse of join matrices on two sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Determinant and inverse of join matrices on two sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Determinant and inverse of join matrices on two sets will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-564634

All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.