Re: ? intersect of two subspaces


"Gerry Myerson" <gerry@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message
news:gerry-8B754B.08512708112006@xxxxxxxxxxxxxxxxxxxxx
In article <1162883784.133515.53400@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Proginoskes" <CCHeckman@xxxxxxxxx> wrote:

Gerry Myerson wrote:
In article <wmS3h.5684$nG1.4283@xxxxxxxxxxxxxxxxxxxxxxxx>,
"Cheng Cosine" <acosine@xxxxxxxxxxxx> wrote:

In 2D, if two lines (2-1=1D subspaces) are not parallel to each
other,
they must intersect.

In 3D, if two planes (3-1=2D) are not parallel to each other, they
must
intersect.

Will the above remain true for any higher dimensional spaces? That
is,

In N-dim, if two ( N-1 ) subspaces are not parallel to each other,
they
must intersect?

I believe that if two subspaces of N-space have dimensions adding up
to N or more, then they must be parallel or intersect.

Since every subspace contains 0, how can two subspaces be parallel? Do
you really mean affine spaces here?

OP's questions don't make sense unless OP is talking affine,
so, yes, that's what I really mean.


I came out these question when I was reading the definition of principal

angles between two subspaces in R^n. But I did not find anything about

affine space in the related texts for the topics of principal angles. Or
does it

mean that when we are talking about subspaces of a linear map, we are
actually

taking about affine space, space withput an origin?

Thanks,
by Cheng Cosine
Nov/07/2k6 NC


.

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