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

**From:** Wolfgang Bangerth (*bangerth_at_[hidden]*)

**Date:** 2006-01-08 12:40:05

**Next message:**Neal Becker: "Re: [glas] norms and inner products for vectors of matrices"**Previous message:**Karl Meerbergen: "Re: [glas] (no subject)"**Next in thread:**Neal Becker: "Re: [glas] norms and inner products for vectors of matrices"**Reply:**Neal Becker: "Re: [glas] norms and inner products for vectors of matrices"**Maybe reply:**Russell Smiley: "Re: [glas] norms and inner products for vectors of matrices"**Maybe reply:**Wolfgang Bangerth: "Re: [glas] norms and inner products for vectors of matrices"

> 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).

Best

W.

-------------------------------------------------------------------------

Wolfgang Bangerth email: bangerth_at_[hidden]

www: http://www.math.tamu.edu/~bangerth/

**Next message:**Neal Becker: "Re: [glas] norms and inner products for vectors of matrices"**Previous message:**Karl Meerbergen: "Re: [glas] (no subject)"**Next in thread:**Neal Becker: "Re: [glas] norms and inner products for vectors of matrices"**Reply:**Neal Becker: "Re: [glas] norms and inner products for vectors of matrices"**Maybe reply:**Russell Smiley: "Re: [glas] norms and inner products for vectors of matrices"**Maybe reply:**Wolfgang Bangerth: "Re: [glas] norms and inner products for vectors of matrices"