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: Diagonalisability problem and others

  1. Feb 22, 2010 #1
    1. The problem statement, all variables and given/known data
    1.Prove that if A is a real matrix then At A is diagonalisable.

    2. Given a known 3*3 matrix A, Calculate the maximum and minimum values of ||Ax|| on the sphere ||x|| = 1.

    2. Relevant equations

    3. The attempt at a solution
    For the first problem, I'm thinking of proving that AtA is symmetric, but I'm not sure which properties to use.
    For the second one, is X a 3*n matrix? Do I need to discuss n?
    Any help is greatly appreciated!
  2. jcsd
  3. Feb 22, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    If [itex]B=A^TA[/itex], write down what [itex]B_{ij}[/itex] and [itex]B_{ji}[/itex] are in terms of the elements of A and show that they're equal.
  4. Feb 23, 2010 #3
    Thanks a lot! I can't believe I missed it in the first place.
    Could anyone give me some hints about problem 2?
  5. Feb 23, 2010 #4


    User Avatar
    Homework Helper

    For the second one, yes, x must be such a vector that the product Ax is meaningful, i.e. a 3x1 vector (matrix).
  6. Feb 23, 2010 #5
    thx, I finished it!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook