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: Showing a Matrix is Symmetric

  1. Oct 25, 2008 #1
    1. The problem statement, all variables and given/known data

    A matrix S is symmetric if S = ST. Show that AAT is symmetric for any matrix A.

    2. Relevant equations

    AAT = (AT)TAT

    3. The attempt at a solution

    I just said:

    A = (AT)T and AT = AT

    Therefore AAT is symmetric.

    I am unsure if that proves it or if I just went in a circle proving nothing.
  2. jcsd
  3. Oct 25, 2008 #2


    User Avatar
    Homework Helper

    If [tex] A, B [/tex] are any matrices, how do you simplify the following expression?


    Apply that answer to simplify

    A A^T

    and use the hints you provided
  4. Oct 25, 2008 #3
    Ok I think this is right.

    (AB)T = BTAT

    Then (AAT)T = AAT

    Therefore AAT is symmetric because (AT)T = A and AT = AT.
  5. Oct 25, 2008 #4


    User Avatar
    Homework Helper

    I think you have the correct idea. the 'conventional' way of finishing the proof would be to write everything in one string rather than stopping midstream - I have no idea how
    picky your professor would be in that regard.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook