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Glas :Re: [glas] norms and inner products for vectors of matrices |
From: Neal Becker (ndbecker2_at_[hidden])
Date: 2006-01-09 06:55:15
On Sunday 08 January 2006 12:40 pm, Wolfgang Bangerth wrote:
> > Talking about vectors of matrices, we need to define algorithms for
> > those: let v be a vector of matrices, so v[i] is a matrix,
> >
> > Then norm_1 could be:
> > sum_i norm_1( v[i] )
> >
> > Norm_inf:
> > max_i norm_inf(v[i])
> >
> > and similarly for other norm functions.
> >
> > For the inner product, trans(v)*w is then
> > sum_i trans(v[i]) * w[i]
> >
> > Is this ok?
>
> Certainly, at least for the norm. For the inner product, should it be
> trans(v[i]) * w[i]
> or
> v[i] * w[i]
> I guess the former makes sense if one thinks of vectors that have a block
> structure (in your diction, each block would be a n times 1 matrix).
>
I think you want v[i] * conj (w[i]).