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

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

**Date:** 2006-01-13 05:02:29

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Peter Gottschling wrote:

>Concerning the norms, I would like to limit the result type to real

>values as I have seen it in all mathematical definitions. Does

>somebody sees a reason to vectors or matrices as results?

>

>The definitions of vector<vector> norms are straight forward:

>- norm_1 := sum (norm_1(x[i])

>- norm_2 := sqrt(sum(norm_2(x[i])^2)) // there might be more

>efficient ways to compute this

>- norm_inf := max(norm_inf(x[i])

>

>Best,

>Peter

>

>

>

>

I am afraid that we cannot define norm_1, etc in this way. (I too made

this mistake in a previous mail) But we can define functions

generalized_norm_1 := sum (generalized_norm_1(x[i])

generalized_norm_2 :=sqrt( sum (generalized_norm_2(x[i])^2 )

generalized_norm_inf := max (generalized_norm_inf(x[i])

norm_1, norm_2, norm_inf are well defined in linear algebra and these

definitions should be respected:

norm_1 := sum( abs(x[i]) )

etc.

These should only be used for vector and matrix objects with 'scalar'

value_type's.

Karl

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