4-D Clifford Algebra with (-1,1,1,1) signature

Weyl Basis: \[\gamma^0=\begin{bmatrix}0&-1\\1&0\end{bmatrix};\; \gamma^i=\begin{bmatrix}0&\sigma^i\\\sigma^i&0\end{bmatrix}\]
Dirac Basis: \[\gamma^0=\begin{bmatrix}i&0\\0&-i\end{bmatrix};\; \gamma^i=\begin{bmatrix}0&\sigma^i\\\sigma^i&0\end{bmatrix}\]
Majorana Basis: \[\gamma^0=\begin{bmatrix}0&i\sigma^2\\i\sigma^2&0\end{bmatrix};\; \gamma^1=\begin{bmatrix}-\sigma^3&0\\0&-\sigma^3\end{bmatrix};\; \gamma^2=\begin{bmatrix}0&-i\sigma^2\\i\sigma^2&0\end{bmatrix};\; \gamma^3=\begin{bmatrix}\sigma^1&0\\0&\sigma^1\end{bmatrix};\;\]
\[\gamma^\mu_{\text{Dirac}}=\begin{bmatrix}\frac{1}{\sqrt{2}}&\frac{i}{\sqrt{2}}\\\frac{i}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{bmatrix}\gamma^\mu_{\text{Weyl}}\begin{bmatrix}\frac{1}{\sqrt{2}}&\frac{i}{\sqrt{2}}\\\frac{i}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{bmatrix}^{-1}\]