# Does the adjoint of an outer product equal to itself?

#### onelastdance

So (|a><a|)† = |a><a|

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#### micromass

Why don't you try to prove it??

#### NegativeDept

A good start might be to try a few test cases. Write down a small (2- or 3-dimensional) complex vector $|a \rangle$ and calculate its outer product with itself. Then check each matrix element to see if the real parts of $| a \rangle \langle a|$ are symmetric and the imaginary parts are anti-symmetric.

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