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Re: What is a projection of an n-tuple?
Posted:
Jan 26, 2013 11:52 AM
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"Peter Percival" <peterxpercival@hotmail.com> wrote in message
news:op.wrivawbc0vm3y5@peter-7xmgui5wz...
> On Fri, 25 Jan 2013 16:24:06 -0000, Tim Golden BandTech.com
> <timgolden@bandtechnology.com> wrote:
>
> > On Jan 24, 3:12 pm, "Peter Percival" <peterxperci...@hotmail.com>
> > wrote:
> >> Writing <...> for an ordered n-tuple; is the second projection of
> >> <x,y,z>
> >> y or <y>?
> >>
> >> --
> >> Using Opera's revolutionary email client:http://www.opera.com/mail/
> >
> > Ha hah. I recommend ditching the standard mathematician's definition
> > of projection.
>
> First I want to know what the standard mathematician's definition of
> projection _is_.
Virgil gave a reasonable definition of this. Another way of saying the same
thing is that applying projection twice in succession has the same result as
applying it once. I.e. if T is the linear map that is a projection, then
T^2 = T.
Your application of projections to n-tuples is maybe a special application,
so I would just read carefully the definition given in the text you're
referring to. Generally, what people talk about is projections in R^n.
E.g. we could have a projection T in R^3 with
T(x,y,z) = (0,y,0).
Note that T^2(x,y,z) = T(0,y,0) = (0,y,0) = T(x,y,z)
i.e. T^2 = T, as we would want for a projection mapping.
So in your case, maybe the author is considering the set of all 3-tuples as
a 3-d vector space, in which case the answer to your final question would
probably be <0,y,0>, but maybe the author has something else in mind.
Mike.
>
> > Consider that you have a high dimension data set
>
> Which I don't.
>
> --
> Using Opera's revolutionary email client: http://www.opera.com/mail/
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