"Peter Percival" <firstname.lastname@example.org> wrote in message news:op.wrivawbc0vm3y5@peter-7xmgui5wz... > On Fri, 25 Jan 2013 16:24:06 -0000, Tim Golden BandTech.com > <email@example.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.
> > > Consider that you have a high dimension data set > > Which I don't. > > -- > Using Opera's revolutionary email client: http://www.opera.com/mail/