1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Linear Mappings & Proofs

  1. Sep 19, 2009 #1
    1. Hi!
    I was wondering if anyone could help me to solve the following problem!
    Let L : [R][n] ->[R][m] and M :[R][m]-> [R][m] be linear mappings.
    Prove that if M is invertible, then rank (M o L) = rank (L)

    thanks!! :)
  2. jcsd
  3. Sep 19, 2009 #2


    User Avatar
    Science Advisor

    If M is invertible it maps Rm one-to-one onto Rm. In particular, it maps any k dimensional subset of Rm onto a k dimensional subset of Rm. Now, what does "rank" mean?
  4. Sep 19, 2009 #3
    the dimension of the column space of M is the rank of M

    and we know that dim (null M)= 0 since the null space of M is just the zero vector
    and since rank = m - (dimension of the null space of M)
    so rank is m?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook