摘要：
By way of analog symmetric polynomial, with primary symmetric polynomial to express a kind ofspecial symmetric polynomial sk(x1,x2,···,xn) = Σn I=1 xk I(k = 0,l,2,···) that approach-Newton's formula, and by n-variable mXm elementary square matrix, a new calculation of the k-th power sum of n-variable mXmsquare matrix Sk= Σn I=1 xk I(k = 0,l,2, ···) is gained, which is similar to Newton's formula. This paper mainlydeals with the discussion of the algorithm of k-th power sum of binary mXm matrix Sk = Σ2 I=1 xk I(k = 0,l,2,···), providing some useful conclusions in the condition that binary mXm elementary square matrix, performs as the special matrix. Although only two formulas of calculating k-th power sum of n-variable m X m matrix are given, a new way of thinking and method is provided to solve this kind of problem.%文中用初等对称多项式来表示特殊对称多项式Sk(x1,x2,…,xn)=∑ni=xki(k=0,1,2,…)方法得到了n元m阶方阵的k次方和Sk=∑ni=Xki(k=0,1,2,…)类似的公式,并对其的计算问题进行了研究,得出了一系列结论.
