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

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

2009-06-20

arxiv.org/abs/0906.3781v1

Mathematics

General Mathematics

8 pages

Scientific paper

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.

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