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

From: Matthias Troyer (troyer_at_[hidden])
Date: 2005-03-29 16:26:55

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

> 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.