Talk:Hermitian adjoint
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Shouldn't one use inner product notation here rather than bra-ket notation?
I.e. 
rather than 
.
PJ.de.Bruin 00:49, 5 Jul 2004 (UTC)
at least one concrete example would be nice! otherwise it seems A*=A^{-1} as in A*A=AA*=I... anyone?
[edit] Hermiticity & Self-Adjointness: Distinction
The distinction is not made clear. A is self-adjoint if:
Hermiticity does not necessarily guarantee the latter statement.
Dirc 20:52, 14 February 2007 (UTC)
- Hermiticity and self-adjoitness are synonymous. (the notation A* = A implicitly implies Dom(A) = Dom(A*), usually.) so doesn't quite make sense to say self-adjointness is not guaranteed by Hermiticity. on the other hand, being symmetric does not imply an operator is self-adjoint/Hermitian in general. Mct mht 23:48, 14 February 2007 (UTC)
[edit] Proof?
Hmm, the article says:
- Moreover,
I don't really see how this follows from the properties above it. Can someone provide a simple proof for this?
- Never mind, think I found it. How dumb can you be?
- A * A is Hermitian, as one can easily show. Therefore
