We study the space that consists of all nonsingular binary matrices, that is, GLn(Z2). The space is quite important in that it is\r\nused for the change of basis in binary representation, which is the encoding typically adopted in genetic algorithms. We analyze\r\nthe properties of GLn(Z2) and theoretically design possible encodings and their corresponding recombination operators for\r\nevolutionary algorithms.We present approaches based on elementary matrices of linear algebra as well as typical two-dimensional\r\nones.
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