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Glas :Re: [glas] norms and inner products for vectors of matrices |
From: Andrew Lumsdaine (lums_at_[hidden])
Date: 2006-01-09 08:24:31
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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