The math behind the Luther-Ives criterion

From ChatGPT. I checked it and it looks right to me. The Luther–Ives criterion states: A three-channel camera is exactly colorimetric if and only if its spectral sensitivity functions span the same three-dimensional function space as the human color-matching functions. 1. Spectral responses Let \(s(\lambda)\) be the spectral power distribution reaching the camera. For the CIE standard observer, define \[ \mathbf{x}(\lambda)= \begin{bmatrix} \bar x(\lambda)\\ \bar y(\lambda)\\ \bar z(\lambda) \end{bmatrix}. \] The corresponding tristimulus values are \[ \mathbf{t} = \begin{bmatrix} X\\Y\\Z \end{bmatrix} = \int_{\Lambda}\mathbf{x}(\lambda)s(\lambda)\,d\lambda. \] Similarly, let the camera sensitivities be \[ \mathbf{q}(\lambda)= \begin{bmatrix} q_R(\lambda)\\ q_G(\lambda)\\ q_B(\lambda) \end{bmatrix}, \] giving the linear raw response \[ \mathbf{c} = \begin{bmatrix} R\\G\\B \end{bmatrix} = \int_{\Lambda}\mathbf{q}(\lambda)s(\lambda)\,d\lambda. \] Dark-current subtraction, linear sensor…