Invertible three-channel opponent transform

The illustrative transform $y_0=c_L+c_M$, $y_1=c_L-c_M$, $y_2=c_S-(c_L+c_M)/2$ has determinant $-2$. Solving gives $c_L=(y_0+y_1)/2$, $c_M=(y_0-y_1)/2$ and $c_S=y_2+y_0/2$. Thus it reorganizes three cone coordinates without adding independent spectral information. Biological response weights and nonlinearities are further empirical questions.