## Glas :## Re: [glas] norms and inner products for vectors of matrices |

**From:** Karl Meerbergen (*Karl.Meerbergen_at_[hidden]*)

**Date:** 2006-01-09 07:12:56

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On Monday 09 January 2006 12:55, Neal Becker wrote:

> > 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]).

Note that the dot product does not have a conjugate transpose.

In a Linear Algebra notation, the (Euclidean) inner product would be

herm(w)*v

which is translated into

sum_i conj(w[i])*v[i]

when w[i] and v[i] are scalars.

Alternative notations could be

trans(conj(w))*v (very unusual)

herm_trans(w)*v

When w and v's value_type's are collections themselves, we would have:

herm(w)*v = sum_i herm(w[i])*v[i]

Assuming that herm(x)=conj(x) for a scalar, this also holds for vectors of

scalars.

Karl

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