# [SciPy-dev] Type handling of matrices

Norbert Nemec Norbert.Nemec.list at gmx.de
Wed Nov 17 03:33:12 CST 2004

On Wednesday 17 November 2004 10:08, Nils Wagner wrote:
> Hi all,
>
> It would be nice to have another "property check"
>
> complex matrices
>
> A.isnormal is true if A^H A - A A^H = 0, that is A commutes with its
>
> real matrices
>
> A.isnormal is true if A^T A - A A^T = 0

Why the special case for real matrices? The hermitian adjoint of a real matrix
is identical to its transposed.

> BTW, how can I compute the gap function of A in scipy, where A is a
> dense normal matrix
> and gap(A) is defined as follows
>
> gap(A) = \min\limits_{i \ne j} | \lambda_i-\lambda_j | / 2
>
> This approach seems to be not very efficient
>
> def gap(A):
>  w = linalg.eigvals(A) # Compute the spectrum of A
>  min = 1.e10 # Initialize
>  for i in len(w):
>   for j in len(w):
>         if i <> j:
>               min1 = abs(w[i]-w[j])
>               if min1 < min:
>                   min=min1
>  return min/2

def gap(A):
w = sort(real(linalg.eigwals(A)))
return min(w[1:]-w[:-1])/2

Don't know about efficiency of the sort, but at least you avoid the loop in
python.

--
_________________________________________Norbert Nemec
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