Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Symmetric matrices maybe

  1. Jul 20, 2009 #1
    I had this question on a test and I was wondering why it is false:

    If the row space equals teh column space then AT=A.
  2. jcsd
  3. Jul 20, 2009 #2
    Consider the matrix
    [tex]\left(\begin{array}{cc}1 & 1\\0 & 1\end{array}\right)[/tex].
  4. Jul 20, 2009 #3
    Ok, so I had a rationale why it was false but I'm not sure if I am close.

    Obviously here the AT does not equal A, but the dimension of the row space equals column space equals 2. Is this the right reasoning?
  5. Jul 20, 2009 #4
    Well, the row space and the column space are both R2, but the matrix is not symmetric.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook