Will the real Q please stand up?

In my 1996 article on units of tristimulus values, I used as a definitional equation Jozef Cohen's Q = A ' N, where N is a radiometric function of k wavelengths and Q is a column vector comprising N's associated tristimulus values. With Cohen, I took as Matrix A (having no units) a set of three column vectors comprising color-matching functions. The relation Q = A ' N then forced Q to have dimensions of power, which was inconsistent with the dimensionlessness of matrix A. Besides this problem, calling A ' N the tristimulus values of N still left them in an unspecified basis, so you could get a wide variety of Q vectors from a single N vector by changing the basis of A. Simply specifying Q = A ' N did not supply enough information to specify tristimulus values uniquely. I now propose to define Q = (A ' P)(-1) A ' N, where k-by-3 matrix P contains the (unscaled) spectra of the primaries. Using this definition resolves both the above problems.

Automated summary

The article discusses the definition problem of tristimulus values units and proposes a new defined equation to address existing issues.