LMS is a color space represented by the response of the three types of cones of the human eye, named after their responsivity (sensitivity) at long, medium and short wavelengths.
It is common to use the LMS color space when performing chromatic adaptation (estimating the appearance of a sample under a different illuminant). It's also useful in the study of color blindness, when one or more cone types are defective.
Typically, colors to be adapted chromatically will be specified in a color space other than LMS. The chromatic adaptation matrix in the von Kries transform method, however, expects the LMS color space. Since colors in any color space can, by definition, be transformed to the XYZ color space, only one additional transformation matrix is required to transform colors from the XYZ color space to the LMS color space.
Since the LMS color space is supposed to model the complex human color perception, no single, “objective” transformation matrix between XYZ and LMS exists. Instead, various Color Appearance Models (CAMs) offer various Chromatic Adaptation Transform (CAT) matrices M as part of their modeling of human color perception.
A color space is a specific organization of colors. In combination with physical device profiling, it allows for reproducible representations of color, in both analog and digital representations. A color space may be arbitrary, with particular colors assigned to a set of physical color swatches and corresponding assigned names or numbers such as with the Pantone system, or structured mathematically, as with Adobe RGB or sRGB. A color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers (e.g. triples in RGB or quadruples in CMYK); however, a color model with no associated mapping function to an absolute color space is a more or less arbitrary color system with no connection to any globally understood system of color interpretation. Adding a specific mapping function between a color model and a reference color space establishes within the reference color space a definite "footprint", known as a gamut, and for a given color model this defines a color space. For example, Adobe RGB and sRGB are two different absolute color spaces, both based on the RGB color model. When defining a color space, the usual reference standard is the CIELAB or CIEXYZ color spaces, which were specifically designed to encompass all colors the average human can see.