For a programming project I need the basis of a two dimensional (complex) Hilbert space. Unfortunately, I am not a mathematician and need help.
I think a basis is $\vec{b_1} = \begin{bmatrix} 1 \newline 0 \end{bmatrix}$ und $\vec{b_2} = \begin{bmatrix} 0 \newline 1\end{bmatrix}$. Is this correct?
Thanks in advance for your help