G-逆矩阵相似分类算法的计算机仿真

Computer Simulation on G-inverse Matrix Similar Classification Algorithm

研究了有限域线性空间的线性变换和可逆变换,分析了可逆变换和可逆矩阵之间的关系,提出了G-逆矩阵的概念,并得到了部分有意义的相关定理,并推导出有限域线性空间的可逆变换的个数是n和p的函数φ(n,p)。计数中,不同的可逆变换有可能代表的是同一等价类,具体有多少个相似类个数目前没有具体的计算公式。采用MATLAB平台仿真有限域上相似等价类的计数问题,把理论上难以证明的问题用计算机仿真实现,为今后进一步研究可逆变换问题打下了坚实的基础。

Researched invertible transform of linear space on finite field,analyzed the relationship between invertible transform and invertible matrix.Based on this,provided the concept of G - invertible matrix and derived some related theories.From the basic work,it can be seen that the number of invertible transform is the function of n and p,that isφ（n,p）.Among the calculating numbers,different invertible transform maybe represent the same classification. But the number of similar equivalence classification does not have any specific formula.Therefore,the counting algorithm of similar equivalence classification can be emulated on MATLAB.It simulates the difficult problem which can not be proved by theory on computer.It provides solid foundation for further study of invertible transform.