Let V be the set of all complex square matrices. For define by .

Using the inner product , find the adjoint of .

I feel I'm missing something because I can't arrive at an answer.

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- November 21st 2008, 05:33 AM0-)Adjoint of a transformation
Let V be the set of all complex square matrices. For define by .

Using the inner product , find the adjoint of .

I feel I'm missing something because I can't arrive at an answer. - November 21st 2008, 11:54 AMOpalg
The adjoint of satisfies the condition for all B, where the angled brackets denote the inner product. If you write this in terms of the trace then it becomes . But the trace has the property that . This means that . From that you should be able to see what is.