Inner product

  • Thread starter devious_
  • Start date
  • #1
310
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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].
 
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Answers and Replies

  • #2
Galileo
Science Advisor
Homework Helper
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Just start writing out the left side using [tex]<a,b>=a^\dagger b[/tex].
 
  • #3
310
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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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