Results 1 to 2 of 2

Math Help - Affine space.

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Affine space.

    Let X be an affine space in F^n and let Y be an affine space in F^k. We look now on the next Cartesian product:

    X x Y = {(x,y)| x in X, y in Y} c F^n x F^k =~F^(n+k)

    Prove that if to think on X x Y as subset of F^(n+k) under the identification:

    ((x_1,...,x_n),(y_1,...,y_k)) =(x_1,...,x_n,y_1,...,y_k)

    so we get an affine space.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    Quote Originally Posted by Also sprach Zarathustra View Post
    Let X be an affine space in F^n and let Y be an affine space in F^k. We look now on the next Cartesian product:

    X x Y = {(x,y)| x in X, y in Y} c F^n x F^k =~F^(n+k)

    Prove that if to think on X x Y as subset of F^(n+k) under the identification:

    ((x_1,...,x_n),(y_1,...,y_k)) =(x_1,...,x_n,y_1,...,y_k)

    so we get an affine space.
    What is your question here? what are X,Y? are they simply subsets? remember that when you talk about affine space you're simply talking about \mathbb{F}^n for some n without the usual vector space structure. Are you by any chance talking about algebraic subsets (zeroes of polynomials)? Please make a clear question!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question on null space/column space/row space of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: December 1st 2011, 01:47 PM
  2. Replies: 1
    Last Post: February 11th 2011, 08:38 PM
  3. Replies: 0
    Last Post: December 30th 2010, 09:36 AM
  4. affine geometry
    Posted in the Geometry Forum
    Replies: 1
    Last Post: October 13th 2010, 03:05 PM
  5. Finding singular points of a curve in affine space
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 29th 2010, 03:35 AM

Search Tags


/mathhelpforum @mathhelpforum