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

**From:** Matthias Troyer (*troyer_at_[hidden]*)

**Date:** 2005-03-29 16:26:55

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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.

>

> 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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