## Glas :## Re: [glas] vector space, banach space and hilbert space concepts |

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

**Date:** 2005-03-30 01:17:16

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Matthias Troyer wrote:

> Hi Karl,

>

> On Mar 29, 2005, at 7:32 AM, Karl Meerbergen wrote:

>

>> I'd rather develop a concept that deals with the creation of objects

>> using dimensional or size information, e.g. DimensionConstructible,

>> which is orthogonal to the VectorSpace, Group, etc concepts. The

>> latter merely describe mathematical properties, while the former

>> describes the construction of a new vector or matrix from its

>> dimensional data. This could be the matrix size, a fixed sparse

>> structure, data about how to distribute the data over a network, etc.

>

>

> I take it that DimensionConstructible does not just construct the

> object from a dimension parameter (vector length) but is more

> generally a factory for objects, e.g. distributed vectors or higher

> dimensional arrays.

Yes. That is what I meant.

>

>

>>

>> For example, an iterative method that does not require the creation

>> of new vectors (or matrices), may require the objects to be models of

>> HilbertSpace. A method as BiCGStab needs auxiliary vectors, for which

>> the creation of new vectors (or matrices) is needed. Such vectors

>> should be models of DimensionConstructible and HilbertSpace.

>

>

> Yes, that would do it.

>

> Matthias

>

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