Results 1 to 2 of 2

Math Help - Rank in Linear Maps

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    20

    Rank in Linear Maps

    Could someone please help me with this question:

    Let S:U -> V, T:V->W be linear maps, where U, V, W are vector spaces over the same field K.
    Prove (i) Rank(TS) <= Rank (S)
    (ii) If V=W and T is non singular, then Rank(TS) = Rank(S)


    Any help would be greatly appreciated!
    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Apr 2008
    Posts
    191
    Quote Originally Posted by pseudonym View Post
    Could someone please help me with this question:

    Let S:U -> V, T:V->W be linear maps, where U, V, W are vector spaces over the same field K.
    Prove (i) Rank(TS) <= Rank (S)
    Hi there,

    We have dim(T(S(U))) \leq dim S(U). Hence rank(TS) = dim(TS(U))= dim(T(S(U))) \leq dim S(U) = rank S.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. linear maps, rank
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 27th 2011, 12:16 PM
  2. Maps / Rank and Nullity question
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: January 16th 2011, 05:13 AM
  3. Linear maps
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: December 10th 2010, 11:38 AM
  4. Linear Maps
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 15th 2009, 09:27 AM
  5. Linear maps. Proving its linear, and describing kernal.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 20th 2008, 12:46 AM

Search Tags


/mathhelpforum @mathhelpforum