Procedures for deriving 3 × 3 matrices for converting color values expressed in terms of one set of primaries to colorimetrically equivalent color values expressed in terms of a different set of color primaries are described below. The procedures can be used to convert *RGB* color values to colorimetrically equivalent CIE *XYZ* color values, CIE *XYZ* color values to colorimetrically equivalent *RGB* color values, and *RGB* color values expressed in terms of a one set of red, green, and blue primaries to colorimetrically equivalent *RGB* color values expressed in terms of a second set of red, green, and blue primaries. Also described is a related procedure for determining the color-matching functions for a given set of red, green, and blue primaries.

A 3 × 3 matrix is a shorthand expression for three simultaneous equations. For example, the matrix expression

is equivalent to the set of simultaneous equations

A matrix for converting *RGB* color values expressed in terms of a set of red, green, and blue primaries to colorimetrically equivalent CIE *XYZ* color values expressed in terms of CIE *X*, *Y*, and *Z* primaries can be derived from the chromaticities of the red, green, and blue primaries and the chromaticity of their *white point*, i.e., ...

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