Results 1 to 2 of 2

Math Help - Prrof: Subspace of a finite dimensional vector space is finite dimensional?Help pleas

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    54

    Proof: Subspace of a finite dimensional vector space is finite dimensional?Help pleas

    Show that any subspace of a finite dimensional vector space is finite dimensional and state theorems used.

    I would think that a subspace of a vector space would have fewer than or the same number of vectors in the basis as the vector space and must therefore be finite dimensional, but this does not use theorems just logic and I think my logic may be skewed. Does a subspace of a vector space have the same basis as the vector space and does this have anything to do with the proof? Can anyone help me prove this?

    Any help would be appreciated. Thanks in advance.
    Last edited by chocaholic; February 25th 2010 at 12:13 AM. Reason: misspelt word
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Swlabr's Avatar
    Joined
    May 2009
    Posts
    1,176
    Quote Originally Posted by chocaholic View Post
    Show that any subspace of a finite dimensional vector space is finite dimensional and state theorems used.

    I would think that a subspace of a vector space would have fewer than or the same number of vectors in the basis as the vector space and must therefore be finite dimensional, but this does not use theorems just logic and I think my logic may be skewed. Does a subspace of a vector space have the same basis as the vector space and does this have anything to do with the proof? Can anyone help me prove this?

    Any help would be appreciated. Thanks in advance.
    Do you know that in an n-dimensional vector space a set of n linearly independent vectors forms a basis for the space? Clearly the answer you are looking for falls out of this.

    If you do not know the result, prove it. It isn't too hard. Just take a your n linearly independent vectors, write them in terms of the basis vectors, and show that any of the basis vectors can be written in terms of these vectors.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finite dimensional vector space
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: October 18th 2011, 10:09 AM
  2. Proofs where V is a finite-dimensional vector space
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 3rd 2010, 12:47 PM
  3. Finite Dimensional Vector Space
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 10th 2010, 11:06 AM
  4. Prove this vector space is not finite-dimensional.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 14th 2010, 04:38 AM
  5. Replies: 1
    Last Post: October 15th 2008, 11:34 AM

Search Tags


/mathhelpforum @mathhelpforum