高斯整数环上矩阵的平方和表示

Representation of Sum of Matrix Squares on Gauss Integral Ring

本文主要研究可表示成高斯整数矩阵的平方和的高斯整数矩阵能表示高斯整数矩阵的平方和的个数。

The main results of this paper are the following, If Gauss integral nxn matrix can be represented as the sum of Gauss integral matrix squares,then it is the sum of at most k=k(n) Gauss integral matrix squares, where k = 3 if n= 2 and k = 2m + 2 if 2m+ 1 <a<2m+1,m = 1,2,3,...