In this following document: https://people.cs.umass.edu/~strubell/doc/quantum_tutorial.pdf
Page 16 says the following about Pauli Z gate
However the right-hand most (ket-bra) side of the equation doesn't seem to evaluate to the 2x2 matrix. Is this a typo in the document or am I doing something wrong?
|1><0| = [0 0
1 0] ---- (1)
|0><1| = [0 1 ---- (2)
0 0]
(1) - (2) = [0 -1
1 0]
```
$\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bra}[1]{\left<#1\right|}$
Looks like a typo while copying from $X$ and $Y$ pauli matrices.
It should be $$\ket{0}\bra{0} - \ket{1}\bra{1}$$