I am thinking that I am using Dirac notation to represent $|0\rangle$ and $|1\rangle$ and we are using column vector but why actually using column vector where first one is $(0 \,1)$ for $|1\rangle$ and $(1 \,0)$ for $|0\rangle$?
I guess the idea of using dirac notation is pretty simple cause for qubit-- we have to define both magnitude and as well as phase.
- As we are going to use interference so there will be phase difference which is one kind of direction so that's another reason.
- As |0> and |1> is mutually exclusive and also linearly independent so we can think about column vector by representing like this-
[![Z-Basis]] : https://i.stack.imgur.com/HdvTI.png
- Also we have to remember one thing that they are normalized.