- #1

devious_

- 312

- 3

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].

[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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