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Linear Algebra, unique minimizer of a quadratic function

  1. Jun 14, 2013 #1
    1. The problem statement, all variables and given/known data
    2013_06_13_20_56_10.jpg

    The part I'm having problems with is where the last two expressions in 4.13 are equated. Why is xtKx*equal to x*^tKx*?




    3. The attempt at a solution
    xtKx* is an inner product and due to symmetry is equal to x*^tKx, but wouldnt equating x to x* mean every <x,y> = <x,x> = <y,y>?

    Many thanks if someone decides to help me out.
     
  2. jcsd
  3. Jun 14, 2013 #2

    haruspex

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    That's not what happened. Try multiplying out the left hand expression of the second line of 4.13.
     
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