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Help me understand a line in an ATA is positive, semi-definite proof

  1. Apr 18, 2012 #1
    help me understand a line in an "ATA is positive, semi-definite" proof

    I am looking at a proof for why ATA is positive semi-definite when A is nxn and it has this line.

    vTAATv = ATv • ATv ≥ 0.

    I understand what vTAATv means and the purpose of proving that it's nonnegative, etc... My problem is that I am a linear algebra novice and do not necessarily understand how the first part vTAATv is equivalent to ATv • ATv. I know that aTb = a • b, but something else is going on, no? Appreciate any help!
  2. jcsd
  3. Apr 18, 2012 #2


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    welcome to pf!

    hi psholder! welcome to pf! :smile:

    (try using the X2 button just above the Reply box :wink:)
    ATv • ATv

    = (ATv)T ATv

    = (vTA) ATv :wink:
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