William Stein wrote:
> On Dec 3, 2007 8:13 AM, Bill Hart <[EMAIL PROTECTED]> wrote:
>> I did try to check that Mathematica was getting the right answer, but
>> I had no luck. I don't know how to convert a mathematica matrix into
>> ordinary matrix form in SAGE, so when I do the comparison it always
>> just says false.
>
> Damn it -- you're right. This isn't the first time I've been bitten by
> this. Mathematica is just doing the componentwise product!
>
> sage: mm = mathematica(n)
> sage: n
> [ 1/20 -1/10 1/20]
> [ -1/10 -37/15 47/30]
> [ 1/20 67/30 -77/60]
> sage: mm^2
> {{1/400}, {1/100}, {1/400}, {1/100}, {1369/225}, {2209/900}, {1/400},
> {4489/900}, {5929/3600}}
> sage: n^2
> [ 3/200 53/150 -131/600]
> [ 8/25 1439/150 -147/25]
> [ -57/200 -419/50 3089/600]
>
>
> Why the frick do so many mathematical software systems define
> A^n for A a matrix to be componentwise powering. Other programs,
> e.g., numpy define A*B on numpy arrays to be componentwise
> multiplication.
>
>
> So -- does anybody know how to raise a matrix to a power in
> Mathematica, since I sure don't.
>
Mathematica treats matrices as lists of lists. Since the product of a
list and another list is the component-wise product, the "*" means
hadamard multiplication.
You probably want the "." operator, which does matrix multiplication:
> {{1, 0}, {0, 1}}.{{1, 2}, {3, 4}}
> {{1, 2}, {3, 4}}
or Dot[{{1,0},{0,1}}, {{1,2},{3,4}}]
Yes, this has bitten me several times too. You could also use:
MatrixPower[{{1,2,3},{4,5,6},{7,8,9}}, 20000]
to compute the matrix product power. For benchmarking, this is probably
the function to use.
-Jason
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