I've started reading Nielsen and Chuang's book on Quantum Computing, and didn't get far. In their first chapter on "Nomenclature and notation", I saw the following expression:
$$ \langle \psi \vert A \vert \psi \rangle \geq 0 $$
Can anybody point me to a reference that can describe what this notation means (as this is something difficult to google)?
Thanks
It's called bra-ket notation. More concretely, what you are seeing is the expectation value.
A mathematician would write, if $A$ is an $n\times n$ matrix and $\psi$ is an $n\times 1$ column vector, $$ \langle\psi|A|\psi\rangle=\psi^*A\psi. $$ In the real case that would be $\psi^TA\psi$. Another very common notation for mathematicians would be $\langle A\psi,\psi\rangle$.
The notation $\langle\psi|A|\psi\rangle$ requires $A$ to be selfadjoint (as it usually is in QM) , because otherwise it is incoherent.