I've just started on QM and I'm puzzled with a lot of new ideas in it.
1.On a recent lecture I've attended, there is an equation says: $\langle q'|\sum q|q\rangle \langle q|q' \rangle =\sum q \delta(q,q')$
I don't understand why $\langle q'|q\rangle \langle q|q' \rangle =\delta (q,q')$
Can you explain this equation for me?
2.Actually, I'm still not clear about the bra-ket notation. I've learnt the bra and the ket could be considered as vectors. Then what are the elements of the vectors?
Thank you very much!