One of the most important research questions in GAs is the explanation of the evolutionary process of GAs as a mathematical object. In this paper, we use matrix linear transformations to do it, first. This new method makes the study on mechanism of GAs simpler. We obtain the conditions under which the operators of crossover and mutation are commutative operators of GAs. We also give an exact schema equation on the basis of the concept of schema space. The result is similar to Stephens and Waelbroeck’s work, but they have novel meanings and a larger degree of coarse graining.