On Wed, May 23, 2012 at 08:50:58AM -0700, meekerdb wrote:
> On 5/23/2012 4:53 AM, Stephen P. King wrote:
> >On 5/23/2012 1:03 AM, Russell Standish wrote:
> >>The definition is a somewhat wordy, but essentially technically
> >>correct, form of the standard definition of a basis in Linear Algebra.
> >>
> >>What is your question, exactly?
> >Hi Russell,
> >
> >    Could you elaborate on the dependence of the basis being given in a 
> > definite order?
> 
> I don't think the order of the basis elements has any significance
> except notationally when a general element is expressed as an
> n-tuple in terms of the basis.
> 
> Brent
> 

Yes - that was my take on the Wikipedia article too - namely that a
coordinate system is an n-tuple or real (or complex) numbers
describing a vector space element.

In other words, a coordinate system is a mapping from V (the vector
space in question) to R^n (or C^n). For such a mapping to be unique,
we need an ordered basis supplied.

Cheers

-- 

----------------------------------------------------------------------------
Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au
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