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[glas] concepts, algorithms etc

From: Karl Meerbergen (Karl.Meerbergen_at_[hidden])
Date: 2005-03-11 05:37:52

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,