Determinant of Large Matrix

Mark Westwood markc.westwood at gmail.com
Thu Jun 7 12:27:39 CEST 2007


Hi James

Mathematica says that the determinant of the integer version of this
matrix is 2774532096, which is another vote for the answer you have.

Mathematica says that the determinant of the 24-digit real version of
your matrix is 2.774532096*10^9, which looks very similar to me.

I'd go with Numpy.

Regards

Mark Westwood


PS 13x13 isn't a large matrix !


On Jun 6, 12:10 pm, James Stroud <jstr... at mbi.ucla.edu> wrote:
> Hello All,
>
> I'm using numpy to calculate determinants of matrices that look like
> this (13x13):
>
> [[ 0.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.]
>   [ 1.  0.  1.  4.  1.  9.  4.  4.  1.  1.  4.  9.  4.  9.]
>   [ 1.  1.  0.  1.  4.  4.  9.  9.  4.  4.  1.  4.  1.  4.]
>   [ 1.  4.  1.  0.  9.  1.  4.  4.  9.  1.  4.  1.  4.  1.]
>   [ 1.  1.  4.  9.  0.  4.  4.  4.  1.  4.  1.  9.  4.  9.]
>   [ 1.  9.  4.  1.  4.  0.  4.  4.  9.  4.  1.  1.  4.  1.]
>   [ 1.  4.  9.  4.  4.  4.  0.  1.  1.  1.  9.  1.  9.  4.]
>   [ 1.  4.  9.  4.  4.  4.  1.  0.  4.  1.  9.  4.  4.  1.]
>   [ 1.  1.  4.  9.  1.  9.  1.  4.  0.  4.  4.  4.  4.  9.]
>   [ 1.  1.  4.  1.  4.  4.  1.  1.  4.  0.  9.  4.  9.  4.]
>   [ 1.  4.  1.  4.  1.  1.  9.  9.  4.  9.  0.  4.  1.  4.]
>   [ 1.  9.  4.  1.  9.  1.  1.  4.  4.  4.  4.  0.  4.  1.]
>   [ 1.  4.  1.  4.  4.  4.  9.  4.  4.  9.  1.  4.  0.  1.]
>   [ 1.  9.  4.  1.  9.  1.  4.  1.  9.  4.  4.  1.  1.  0.]]
>
> For this matrix, I'm getting this with numpy:
>
>   2774532095.9999971
>
> But I have a feeling I'm exceeding the capacity of floats here. Does
> anyone have an idea for how to treat this? Is it absurd to think I could
> get a determinant of this matrix? Is there a python package that could
> help me?
>
> Many thanks for any answers.
>
> James





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