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: Matrix proof

  1. Oct 29, 2012 #1
    Define T: Mn×n → Mn×n by T (A) = At . Show
    that R(T) = Mn×n.

    Alright then. The transformation is saying that it's transforming an nxn matrix into an nxn matrix (duh).

    T(A)=A^t thus A^t is still an nxn matrix.

    Thus R(T) is all of Mnxn?

    Is that it?
  2. jcsd
  3. Oct 29, 2012 #2
    Also another part of the question is:
    Define T: Mn×n → Mn×n by T (A) = A − A^t .
    a. Find R(T ).
    b. Find N(T ).

    a) R(T) is just the right hand side (A-A^t) which is the set of all skew symmetric matrices?

    b) To find N(T) I set the RHS equal to 0. so A-A^t=0 thus A=A^t
    so N(T) is the set of all symmetric matrices?
  4. Oct 29, 2012 #3


    User Avatar
    Science Advisor
    Homework Helper

    Yes for both. You seem to have a pretty good idea what you are doing. You might not need to post ALL of these questions.
  5. Oct 29, 2012 #4
    I'm insecure about most of my answers, even if a lot of them are right.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook