Results 1 to 4 of 4

Math Help - trivial nullspace, basis.

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    15

    trivial nullspace, basis.

    If the nullspace of a transformation is trivial, then is a basis for the nullspace the emptyset?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member HappyJoe's Avatar
    Joined
    Sep 2010
    From
    Denmark
    Posts
    234
    Yes.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,603
    Thanks
    1421
    I would have said "a trivial space (a space consisting of the 0 vector only) does not have a basis" rather than saying "the basis is the empty set".
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member HappyJoe's Avatar
    Joined
    Sep 2010
    From
    Denmark
    Posts
    234
    I suppose it is a matter of convention.

    I prefer the convention that the trivial vector space has the emptyset as basis, partly because then we have no exceptions to the statement "all vector spaces have a basis", and partly because the number of elements in the emptyset is 0, coinciding with the usual idea that the dimension of a point is 0 (and thus being consistent with the dimension of vector spaces being equal to the number of elements in a basis).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Basis for the Nullspace of A
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 24th 2010, 01:03 AM
  2. Nullspace and basis
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: June 20th 2010, 04:42 AM
  3. Basis for left nullspace
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 22nd 2010, 11:27 PM
  4. Find the basis of the nullspace
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 21st 2009, 12:50 PM
  5. Linear algebra: Basis, Nullspace, Subspace
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 1st 2007, 09:33 PM

Search Tags


/mathhelpforum @mathhelpforum