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Homework Help: A certian Linear Algebra gimmick needed for a part of my project

  1. Jan 14, 2014 #1
    1. I need to prove that for any matrix A(n,n) and a vector v(n,1) the following is true...


    So far I wasn't able to think of anyway for proving this... any help will be appreciated.
  2. jcsd
  3. Jan 14, 2014 #2
    I do understand intuitively how this can be true...
    Because of the arrangement of the equation, both side of the equation gets the same value.
    I am able to show that with small example,,

    p & q\\
    r & s
    a & b\end{array}\right]

    \Rightarrow v'Av=v'A'v=a^{2}p+abr+abq+b^{2}s

    But I need rigorous proof for the same...

    Thank you. :)
  4. Jan 14, 2014 #3


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    Homework Helper

    What is the dimension of vTAv and vTATv?
    What is (vTAv)T? How do you transpose a matrix product?

  5. Jan 14, 2014 #4


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    Science Advisor
    Homework Helper

    For two matrices A and B, ##\left(AB\right)^T=B^TA^T##. If you don't already know that prove it using sigma notation.
  6. Jan 14, 2014 #5
    So this is what I understand...

    since the equation [tex]v'Av[/tex] is a number... we can write...


    Am I correct?
  7. Jan 14, 2014 #6


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    Homework Helper

    Yes, that was I wanted you to do.

  8. Jan 14, 2014 #7


    Staff: Mentor

    aashish.v, when you post a problem, include your work in the inital post. Without the work you show in your 2nd post, your 1st post would normally earn you a warning for an unacceptable homework request.
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