Results 1 to 2 of 2

Math Help - Are these subspaces?

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    82

    Are these subspaces?

    For each of the following subsets of the indicated vector space V , decide whether it is a subspace.


    1. GLn(F) in V = Mn(F).
    2. The set Symn V = Mn(F) of symmetric matrices: Symn = {A Mn(F) | AT = A}.
    3. For fixed A V = Mn(F), the centralizer of A C(A) = {B Mn(F) | AB = BA}.
    4. The set of all functions f V = C(R) for which f(1) Q.


    I missed this class and am not really sure how to determine if something is a subspace so I'm trying to do some practice. Any help would be great.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by amm345 View Post
    For each of the following subsets of the indicated vector space V , decide whether it is a subspace.


    1. GLn(F) in V = Mn(F).
    2. The set Symn V = Mn(F) of symmetric matrices: Symn = {A Mn(F) | AT = A}.
    3. For fixed A V = Mn(F), the centralizer of A C(A) = {B Mn(F) | AB = BA}.
    4. The set of all functions f V = C(R) for which f(1) Q.


    I missed this class and am not really sure how to determine if something is a subspace so I'm trying to do some practice. Any help would be great.

    In every case you've to check whether the given set is non-empty, closed under addition and multiplication by scalar. For example in (1), if we aded two invertible matrices do we always get an invertible matrix? Of course not, but now you find a counterexample.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. subspaces...
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 28th 2011, 01:20 PM
  2. Replies: 0
    Last Post: October 13th 2009, 04:48 PM
  3. Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 8th 2009, 10:18 AM
  4. Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 26th 2009, 07:55 PM
  5. Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: March 14th 2009, 06:50 PM

Search Tags


/mathhelpforum @mathhelpforum