C. P. Williams, Explorations in Quantum Computing. in Texts in Computer Science. London: Springer, 2011. doi: 10.1007/978-1-84628-887-6.
Defining a unitary matrix, where $U^{-1} = U^\dagger $ (inverse equals its conjugate transpose).
Pauli matrices:
$1 = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$
$X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$
$Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}$
$Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$
NOT gate:
Hadamard Gate:
