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

From: Michael A Heroux (maherou_at_[hidden])
Date: 2005-03-25 13:21:28


Thanks for your reply. Here are some responses.

> I think we have had several rounds where requirements were
> requested, with very little input, unfortunately. The best
> document so far is the charter that was distributed from the
> start, as far as I can see. Perhaps we should redistribute
> the document and ask everyone if something is missing. I
> think Toon has the latest version, but he is on holiday.
> Perhaps the document should be rewritten, e.g. a bullet list
> with very concrete objectives.

I think a reasonable goal is to make sure that major specification/design
elements can be traced back to requirements. I took a look at Toon's GLAS
requirements document dated 19-Dec-2004 and read through the discussion that
followed. It looks like much of the spec/design of the concepts and models
is not explicitly traceable to the requirements document or the discussion,
which means that the design or the requirements, or both, should be
discussed and modified.

> I agree that there are many concepts, but this is a result
> that emerged from discussions on the mailing list. Everyone
> has different backgrounds, and it is not easy to define
> concepts that meet everyone's expectations, hence the large
> number. Also note that I have tried to make these concepts
> correspond to mathematical definitions. I think that if we
> use a concept vectorspace, it should correspond to the math
> concept, otherwise it should get another name.
> Some people talk about vectorspace when they mean
> hilbertspace. It creates confusion to those who have yet
> another interpretation of math concepts.

As part of the discussion of traceability, I think it would be worth
determining how closely we want to model the rich mathematical structure
that you have developed. Is there a practical purpose for have Group, and
four variations of Group? If so, this should be stated in the requirements.

> This is very useful information. We have similar objects in
> our code. I wonder whether vectorspace is the correct name
> for this concept. Should it not be something related to
> dimensions or sizes? For example, VectorSize,
> VectorSpaceSize. I do not want to use the name dimension,
> because this corresponds to the dimension of the vectorspace
> which is not necessarily the same as the size of a vector/matrix.

Perhaps I am wrong, but I have always considered dimensionality of a vector
space (at least a finite dimensional vector space, which is the only kind we
can handle with today's memory limits :>) the same as the length of a member
vector. N-dimensional Euclidean space is the most common example of a
vector space. It seems reasonable to me that 3-dimensional Euclidean space
is different that 4-dimensional Euclidean space. If this is true then I
think it is also reasonable to have a two vector spaces associated with a
linear operator. For example, a 3-by-4 matrix would have the previous two
spaces. However, maybe I am missing your point.

Best regards,