Does the adjoint of an outer product equal to itself?

[onelastdance]

So (|a><a|)† = |a><a|

 

[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.