Quote:
Originally Posted by Kyler
Okay, I have created a basic program to make the n X n matrix as defined in the post that sort of explains the rankings but what do I do from there? I am only in trig and we have definitely not learned that stuff with matrices. Can somebody give me an example of "M(k1)p(1)+M(k2)p(2)+...+M(kn)p(n) should equal s(k)" or clarify that please? Thanks!
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From there you need to invert M and multiply it by
s. The are libraries doing the first all over the internet - however, I do not know the algorithm they use. I know how to do it manually, but that would take way too much time for anything this scale.
Then you need to multiply M inverse by
s. What you're looking to get out is another column vector, or list of numbers, similar to the one you have in
s, although with different numbers. To do that, simply multiply each element in a column of M inverse (with a fixed row) by each element in the corresponding row in
s (which has only one column). For example, to find the 10th element of
p, or the average number of points contributed by the team in the 10th row, add up M(10,1)*
s(1) + M(10,2)*
s(2) + M(10,3)*
s(3) + ...
Doing that for each row in M will get you
p, the vector you're looking for.
If this didn't make much sense, look at
http://mathdemos.gcsu.edu/mathdemos/matvec/matvec.html or
http://en.wikipedia.org/wiki/Matrix_multiplication