# Elementary question: is $\langle a|b \rangle$ the same as $\langle a||b\rangle$?

In trying to learn more about quantum computing, one of the first things encountered is a definition of the inner product $$\langle a|b\rangle$$. If I interpret it correctly, and looking near the bottom of page 15 of the 2011 book by Rieffel and Polak, this notation is shorthand for writing $$\langle a||b\rangle$$. Is that correct, or is my understanding flawed?

It may seem as though it is obvious (or obviously wrong), but so far I have found it strangely rare to see this explicitly stated. I would welcome some confirmation or correction.

Your understanding is correct. $$\langle a | b \rangle$$ is shorthand for $$\langle a||b\rangle$$. Here is a good resource for linear algebra and Dirac notation for quantum computing.