On Oct 15, 2010, at 11:37 AM, Ganesh Natrajan wrote: > Douglas, > > The elements of a 'vector space' are not 'vectors' in the physical > sense.
And there you make Ed's point -- some people are using the general vector definition, others are using the more restricted Euclidean definition. The elements of a general vector space certainly can be physical, by any normal sense of the term. And note that physical 3D space is not Euclidean, in any case. > The correct Wikipedia page is this one > > http://en.wikipedia.org/wiki/Euclidean_vector > > > Ganesh > > > > On Fri, 15 Oct 2010 11:20:04 -0400, Douglas Theobald > <dtheob...@brandeis.edu> wrote: >> As usual, the Omniscient Wikipedia does a pretty good job of giving >> the standard mathematical definition of a "vector": >> >> http://en.wikipedia.org/wiki/Vector_space#Definition >> >> If the thing fulfills the axioms, it's a vector. Complex numbers do, >> as well as scalars. >> >> On Oct 15, 2010, at 8:56 AM, David Schuller wrote: >> >>> On 10/14/10 11:22, Ed Pozharski wrote: >>>> Again, definitions are a matter of choice.... >>>> There is no "correct" definition of anything. >>> >>> Definitions are a matter of community choice, not personal choice; i.e. a >>> matter of convention. If you come across a short squat animal with split >>> hooves rooting through the mud and choose to define it as a "giraffe," you >>> will find yourself ignored and cut off from the larger community which >>> chooses to define it as a "pig." >>> >>> -- >>> ======================================================================= >>> All Things Serve the Beam >>> ======================================================================= >>> David J. Schuller >>> modern man in a post-modern world >>> MacCHESS, Cornell University >>> schul...@cornell.edu >> >> >> >>
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