Real independence of Clifford-generated vectors
= Real independence of Clifford-generated vectors
For hermitian generators satisfying $\{\gamma^I,\gamma^J\}_+=2\delta^{IJ}$ and any nonzero vector $v$, the vectors $\gamma^Iv$ are linearly independent over the real numbers. Indeed, $A=\sum_Ia_I\gamma^I$ with real $a_I$ obeys $A^2=(\sum_Ia_I^2)\mathbf1$, so $\|Av\|^2=(\sum_Ia_I^2)\|v\|^2$. Complex coefficients need a different argument.