3

1

For example:

$$\rm{X=\sigma_x=NOT=|0\rangle\langle 1|+|1\rangle\langle 0|=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}}$$

$$\rm{Z=\sigma_Z=signflip=|0\rangle\langle 0|-|1\rangle\langle 1|=\begin{bmatrix}1 & 0 \\ 0 & -1\end{bmatrix}}$$

I do no understand how the matrix can be expressed in bra-ket and the way around. I could not find any good teachings on this.

please try to use mathjax rather than images whenever possible

– glS – 2020-10-09T06:55:09.223@glS no, my question is answered below as you can see checked it as an answer. – John T – 2020-10-09T09:07:34.023