特征多项式系数的多种解析

Multiple Interpretations of Eigenpolynomial Coefficients

利用矩阵特征多项式系数,可以帮助解决许多矩阵求解问题.因此,现有许多从某一方面出发、围绕特征多项式系数展开的研究.研究从多方面对特征多项式的系数特点做出了分析归纳,分别用矩阵的k阶主子式的和、矩阵的特征值、矩阵乘积的迹及矩阵A的次幂的迹表示特征多项式系数,得出了规律性的结论,同时对与特征多项式系数有着密切联系的牛顿等幂和公式给出了证明.

The coefficients of matrix eigenpolynomials can help solve many matrix solving problems.So many literatures have been studied around eigenpolynomial coefficients from a certain aspect.In this study,the coefficient characteristics of the eigenpolynomial are analyzed and summarized from many aspects,and the eigenpolyal coefficients are expressed by the sum of the korder principal and sub-formulas of the matrix,the eigenvalue of the matrix,the trace of the matrix product and the trace of the matrix A,some regular conclusions are drawn,and the Newtonian power sum formula,which is closely related to the eigenpolynomial coefficient is proved.