整数环上矩阵平方和的两个新结论

Two New Results of Sums of Square Matrices in Integer Ring

本文利用 F2 上方阵为平方矩阵的充要条件 ,证明了 :1任一阶数为偶数的整数矩阵可表示成 5个平方次幂整数矩阵之和 ;2任一整数矩阵可表示成 6个平方次幂整数矩阵之和 ,从而改进了文 [2 ,3 ]的主要结论 .

In this paper, by using the necessary and sufficient coindition of a square matrix in the fields of characteristic 2 we have proved the following results: 1) Every integer matrix which order is even number can be expressed as sums of 5 square integer matrices. 2) Every integer matrix of order n can be expressed as sums of 6 square integer matrices. The results of the article improve main results in .