Quote:
Originally Posted by kirtar
Somewhat resurrecting a dead thread but.... Does the matrix on that sheet even work with Cholesky Decomposition? I entered it into Mathematica and an online calculator and both returned errors (possibly because of those zeroes in there...). If the reason is because of the zeroes, won't that not work because you're not going to be playing with every team and there will be some zeroes in the chart (then again, since I don't exactly understand how the decomposition works, I could easily be very wrong).
Also, for those using inverse matrices, what happens when the matrix does not have an inverse  ? Don't think it'll happen, but, it's a possibility (btw the example on the posted sheet also does not have an inverse). Even better... If we're keeping track of relatively detailed robot performance anyways, does it even matter? |
Because of the way our matrices are assembled, as long as every team has played at least one match, the matrix is invertable. That is because the diagonal terms are the number of matches that team played, which is why OPR can not be calculated until you have some matches done. Otherwise you will have some zeroes at the diagonal terms and it will make your matrix become singular and can not be inverted.
Ed