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

**From:** Andrew Lumsdaine (*lums_at_[hidden]*)

**Date:** 2006-01-09 08:24:31

**Next message:**Karl Meerbergen: "Re: [glas] norms and inner products for vectors of matrices"**Previous message:**Karl Meerbergen: "Re: [glas] norms and inner products for vectors of matrices"**In reply to:**Neal Becker: "Re: [glas] norms and inner products for vectors of matrices"**Next in thread:**Karl Meerbergen: "Re: [glas] norms and inner products for vectors of matrices"**Reply:**Karl Meerbergen: "Re: [glas] norms and inner products for vectors of matrices"

I think the definition of the norm for a vector of matrices depends

on what is meant mathematically by a vector of matrices. If the

vector of matrices is a block row (or block column) sliced out of a

block matrix, then the definitions shown would not be the expected

norms for that portion of the matrix without the blocking. And I

think, at least in some cases, one would want those norms to be the

same.

On Jan 9, 2006, at 6:55 AM, Neal Becker wrote:

> 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]).

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**Next message:**Karl Meerbergen: "Re: [glas] norms and inner products for vectors of matrices"**Previous message:**Karl Meerbergen: "Re: [glas] norms and inner products for vectors of matrices"**In reply to:**Neal Becker: "Re: [glas] norms and inner products for vectors of matrices"**Next in thread:**Karl Meerbergen: "Re: [glas] norms and inner products for vectors of matrices"**Reply:**Karl Meerbergen: "Re: [glas] norms and inner products for vectors of matrices"