## Glas :## [glas] concepts, algorithms etc |

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

**Date:** 2005-03-11 05:37:52

**Next message:**David Abrahams: "Re: [glas] concepts, algorithms etc"**Previous message:**Toon Knapen: "[glas] Re: [boost] Re: Fixed Size Matrix"**In reply to:**Kevin Wheatley: "Re: [glas] Vector Spaces vs. "Objects called vectors""**Next in thread:**David Abrahams: "Re: [glas] concepts, algorithms etc"**Reply:**David Abrahams: "Re: [glas] concepts, algorithms etc"**Reply:**Karl Meerbergen: "[glas] vector space, banach space and hilbert space concepts"**Reply:**Karl Meerbergen: "Re: [glas] concepts, algorithms etc"

Hello All,

It has been a long time since there was some activitity on the mailing

list. We are still struggling with defining concepts and algorithms. I

propose something to make our life easier.

Some people suggested to introduce a VectorSpace concept. I do not

believe that this is necessary, because it is far too narrow. In fact,

linear algebra vectors are usually employed as basis vectors for a

vector space so they actually already define a vector space.

Note that we also may have to introduce Euclidean spaces for inner

products, but this is also too narrow, since it does not cover the dot

product for complex values for example.

And then we have not talked about matrices. I do not want concepts to be

limited to vector spaces and Euclidean vector spaces only, they should

be larger.

I think a better starting point is to use definitions and concepts as

much as possible from the book Golub & Van Loan, Matrix Computations 3rd

Edition, The John Hopkins University Press, 1996. Note that this book is

considered the Bible in linear algebra (well, a recent version of the

bible perhaps, more recent than the work by Wilkinson and Householder).

From the point of view of standardization and visibility in the linear

algebra community, I believe this could be a very strong plus for glas.

This book mainly uses real value types, but this can be extended to any

field. So I suggest to require value types to be fields, and then we can

start from this book. It also may reduce our documentation effort,

because we just have to refer to chapters, sections, algorithms,

definitions etc.

Have a nice day,

Karl

**Next message:**David Abrahams: "Re: [glas] concepts, algorithms etc"**Previous message:**Toon Knapen: "[glas] Re: [boost] Re: Fixed Size Matrix"**In reply to:**Kevin Wheatley: "Re: [glas] Vector Spaces vs. "Objects called vectors""**Next in thread:**David Abrahams: "Re: [glas] concepts, algorithms etc"**Reply:**David Abrahams: "Re: [glas] concepts, algorithms etc"**Reply:**Karl Meerbergen: "[glas] vector space, banach space and hilbert space concepts"**Reply:**Karl Meerbergen: "Re: [glas] concepts, algorithms etc"