What is the relationship between color spaces (RGB, XYZ) and color matching? Let's say we have some color matching function in the XYZ color space (three-row matrix). We also have a transformation matrix that translates from XYZ coordinates to RGB coordinates.
I understand that there is some visual input that consists of the color spectrum S (y). The human eye does not see the world - it only sees its interpretation of the world. The human eye has 3 types of LMS cones, each of which is responsible for processing RED, GREEN or BLUE. The human eye sees spectral color only because its eye is summed over RED, GREEN, BLUE vector, and this sum corresponds to the color of the input. To match the color, there is a color matching function that takes an input spectrum and produces a weight to multiply the basic RED, GREEN, BLUE color vector. Then they are added, and their result visually corresponds to the spectral input, although there were many many added frequencies in the spectrum, while the human eye added only 3. Thus, we moved from the HUGE space to space,where we can describe everything with 3 vectors summarized as dictated by the color matching function.
The spectral input, primary colors and color matching functions behave as described above, and can be summarized in this formula:
where pi is the 3D vector of primary colors, c is the color matching function is also a vector of three components, and finally s is the spectral input.
We have the XYZ color space and the corresponding color matching function that does what is described above. Then we get the matrix T, which converts the XYZ coordinates to RGB coordinates. We already know T, and we need to use it to create a new color matching function for the RGB color space.
I do not understand how color space relates to the choice of primaries pi (Ξ») and the choice of color functions ci (Ξ»1).