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
> <[log in to unmask]> 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
>>> [log in to unmask]
>>
>>
>>
>>
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