整数矩阵的方幂和表示

SUMS OF POWERS OF INTEGER MATRICES

本文解决了在代数整数环上的矩阵的乘方和表示问题。对整数环上矩阵的乘方和表示问题作了进一步探讨。对高斯整数环上矩阵的平方和表示的可能性得出了肯定的结果。

The principle result of this paper is as follows: Every Algebraic Number n×n Matrix is the sum of at most n+ i Algebraic Number Matrix in m-th power. This is the open problem (c) proposed by Morris Newman.We also discuss the sums of squares of Gauss integer matrices. We get a necessary and sufficient condition for this posibility. In the case of integral matrix, we prove that every n×n integral matrix is the sum of at most k (m) integral matrices in m-th power, here 4×m.