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Based on a brief review on developments of number system, a new developedpattern 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 tonumber 1 and three units of imaginary number i,j,k, respectively. They formusually a ring. But some fields may be composed of some special 2-rank, evenn-rank matrices, for example, three matrices aI+bC, aI+cB, aI+dA and so on. Itis a new type of hypercomplex number fields. Finally, the physical applicationsand possible meaning of the new number system is researched.

New Developed Pattern on Number System, New Number Field and Their Applications in Physics