一类特殊矩阵中2矩阵与其和矩阵特征向量关系

Relationship Between Matrix 2 and Its Sum Matrix Eigenvectorsin a Special Type of Matrix

在有干扰的条件下,为从具有正弦波特征的采样数据求取一次谐波系数,设计了滤波程序。通过对干扰误差对谐波系数影响机理的分析,得到了一个特殊的由三角函数值构成的二阶矩阵,矩阵的特征值和特征向量决定了计算效率,两个干扰对应两个子矩阵,其和矩阵与子矩阵的特征值及特征向量构成了有趣的关系。一类特殊的,当自变量分别为α和β,构成2个矩阵,其和矩阵的特征向量与这2个矩阵的特征向量呈现出简单的函数关系。为动平衡机干扰信号的消除提供了数学基础。

In the presence of interference,we designed a filtering program to obtain the first harmonic coefficient from sampled data with sine wave characteristics.By analyzing the impact mechanism of interference errors on harmonic coefficients,a special second-order matrix composed of trigonometric function values was obtained.The eigenvalues and eigenvectors of the matrix determine computational efficiency.Two interferences correspond to two sub matrices,and the eigenvalues and eigenvectors of its sum matrix and sub matrices form interesting relationship In a special type of matrix,when independent variables areαandβrespectively,two matrices are formed,the eigenvectors of its sum matrix show simple functional relationship with the eigenvectors of the two matrices,which provides a mathematical basis for eliminating the interference signals of dynamic balancing machines.