Results 1 to 2 of 2

Math Help - Full Column rank of a partitioned matrix

  1. #1
    Junior Member
    Joined
    Aug 2009
    Posts
    30

    Full Column rank of a partitioned matrix

    Suppose matrix X is partitioned into X=[A \ \ \ B] where A is n \times k_1 and B is n \times k_2

    How can I show that if X has full column rank, then X_2 will have full column rank as well
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jun 2008
    Posts
    7
    Hello

    Note, that since X has full column rank, all their columns are linearly independent as vectors; any subset of a linearly independent set of vectors, is linearly independen too. From this your result follows inmediately.

    Best regards.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. question involving matrix row column rank proof
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 8th 2011, 08:28 AM
  2. Replies: 3
    Last Post: August 20th 2010, 06:32 AM
  3. Rank of partitioned matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 9th 2010, 05:21 AM
  4. Short proof that rows-rank=column-rank?
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: June 26th 2009, 11:02 AM
  5. full-rank matrix problem
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 13th 2008, 11:59 AM

Search Tags


/mathhelpforum @mathhelpforum