Choosing a programming language as a competitive tool
paul.magwene at yale.edu
Tue May 8 16:00:38 CEST 2001
"Isaac To Kar Keung" <kkto at csis.hku.hk> wrote in message
news:7i4ruwigff.fsf at enark.csis.hku.hk...
> >>>>> "Greg" == Greg Ewing <see at my.signature> writes:
> Greg> But a collection of coordinates are just one way of representing
> Greg> vector. The abstract concept of a vector doesn't depend on
> Greg> coordinates.
> That's not the mathematical meaning of vector. It's the "physical" or
> "engineering" meaning. The mathematical meaning of vectors has to do with
> linear algebra. While a vectors can still have many "representation" when
> different "basis" is used, it is consistent that multiple real numbers are
> used to represent a vector.
That's not true! We can just as well talk about complex vector spaces as
real vector spaces. In fact, often times it's more convenient to do so
(because the results are more general).
See Sheldon Alexander's book "Linear Algebra Done Right" (1997, Springer)
for a good example of a text that derives many of the common results for
complex vector spaces....
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