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Homework Help: Inner product

  1. Nov 6, 2006 #1
    Is there a non-ugly proof of the following identity:
    [tex]\langle Ax,y \rangle = \langle x,A^*y \rangle[/tex]
    where A is an nxn matrix over, say, [itex]\mathbb{C}[/itex], A* is its conjugate transpose, and [itex]\langle \cdot , \cdot \rangle[/itex] is the standard inner product on [itex]\mathbb{C} ^n[/itex].
     
    Last edited: Nov 6, 2006
  2. jcsd
  3. Nov 6, 2006 #2

    Galileo

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    Just start writing out the left side using [tex]<a,b>=a^\dagger b[/tex].
     
  4. Nov 6, 2006 #3
    Thanks.

    Although using my definition for the standard inner product I had to use [itex] \langle a , b \rangle = a^t \bar{y}[/itex], but it all worked out in the end.
     
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