  Based on a brief review on developments of number system, a new developed
pattern is proposed. The quaternion is extended to a matrix form aI+bC+cB+dA,
in which the unit matrix I and three special matrices C,B,A correspond to
number 1 and three units of imaginary number i,j,k, respectively. They form
usually a ring. But some fields may be composed of some special 2-rank, even
n-rank matrices, for example, three matrices aI+bC, aI+cB, aI+dA and so on. It
is a new type of hypercomplex number fields. Finally, the physical applications
and possible meaning of the new number system is researched.
