1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Matrix rank proof

  1. Oct 4, 2008 #1
    I'm trying to show that any matrix X with rank n can be written as the sum of matrices Z and Y with rank n-1 and 1, respectively.

    Since X,Y, Z have the same dimensions, is this a simple matter of saying pick one of the columns in X with a pivot. Let Z= X with this column replaced by zeroes but all other entries the same as X. Let Y consist of the removed column and all other entries 0. Thus, X=Y+Z and Y has rank n-1 and Z has rank 1.

    Does this look correct?
     
  2. jcsd
  3. Oct 5, 2008 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Yes, that's fine.
     
  4. Oct 5, 2008 #3
    it doesnt seem like this is the most formal logic in the world...is it trivial that the matrices constructed have ranks of n-1 and 1 or does this need to be shown as well
     
  5. Oct 5, 2008 #4

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Since the rank of X is n, its columns are linearly independent. Hence any subset of those columns is linearly independent as well.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Matrix rank proof
  1. Matrix rank proof (Replies: 4)

  2. Rank of a matrix proof (Replies: 2)

  3. Matrix rank proof (Replies: 14)

  4. Rank of a matrix (Replies: 7)

Loading...