The definition is a somewhat wordy, but essentially technically
correct, form of the standard definition of a basis in Linear Algebra.

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What is your question, exactly?
Cheers
On Tue, May 22, 2012 at 09:09:07AM -0400, Stephen P. King wrote:
> Hi Folks,
>
> Lizr's resent post got me thinking again about the concept of a
> basis and reading the wiki article brought up a question.
>
> http://en.wikipedia.org/wiki/Basis_%28linear_algebra%29
>
> "In linear algebra <http://en.wikipedia.org/wiki/Linear_algebra>, a
> *basis* is a set of linearly independent
> <http://en.wikipedia.org/wiki/Linear_independence> vectors
> <http://en.wikipedia.org/wiki/Vector_space> that, in a linear
> combination <http://en.wikipedia.org/wiki/Linear_combination>, can
> represent every vector in a given vector space
> <http://en.wikipedia.org/wiki/Vector_space> or free module
> <http://en.wikipedia.org/wiki/Free_module>, or, more simply put,
> which define a "coordinate system" /_*(as long as the basis is given
> a definite order*_/)."
>
> The reference to that phrase that I have highlighted was
> unavailable, so I ask the resident scholars here for any comment on
> it.
>
> --
> Onward!
>
> Stephen
>
> "Nature, to be commanded, must be obeyed."
> ~ Francis Bacon
>
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