[SciPy-User] raising a matrix to float power
Charles R Harris
charlesr.harris@gmail....
Sun Jul 11 12:41:39 CDT 2010
On Sun, Jul 11, 2010 at 11:31 AM, Alexey Brazhe <brazhe@gmail.com> wrote:
> Seems to be, but not for any matrix:
>
> #-----------------
>
> def mpower(M, p):
> "Matrix exponentiation"
> e,EV = linalg.eigh(M)
> return dot(EV.T,
> dot(diag((e)**p), EV))
>
> m = array([[1.0,2.0], [3.0,4.0]])
>
> then dot(m.T,m) does equal mpower(mpower(dot(m.T,m), 0.5), 2.0)
>
> But mpower(mpower(m,0.5),2) doesn't equal m!
>
>
For this algorithm the matrix needs to be Hermitean, which is the case for
W^T W. More generally, the matrix needs to be normal, i.e., commute with
it's transpose. A matrix can be diagonalized iff it is normal.
<snip>
Chuck
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