On Tuesday, July 3, 2012 10:53:23 AM UTC+1, Dima Pasechnik wrote:
>
> well, it's not that small, especially for finite fields. E.g. for F_2 and
> n=3, one only gets 168 invertible matrices out of 512=2^9 in total...
> (I can't resist saying that the order of GL(n,q) is
> (q^n-1)(q^{n-1}-1)...(q^2-1)(q-1))
> So it's not gonna be very fast, also note that computing the determinant
> comes at a nonzero cost when matrices are big...
>
I stand corrected. Even in the worst case scenario (with F_2) it still
seems that about one in three matrices is invertible, so the situation is
not too bad. Also, there is no need to compute the determinants, knowing
if the rank is full or not is enough. So my point is: even if not *very*
fast, still seems faster than what we have now, and it is very easy to
implement while we think of a better solution.
Javier
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