带参数矩阵特征方程的性质探讨

Properties of Characteristic Equation of Matrix with Parameter

利用与文[1]相类似的方法,探讨了带参数矩阵的特征方程存在纯虚特征根的性质,进一步讨论了当n=5和n=6时实系数齐次线性微分方程组的矩阵具有纯虚特征根的条件,得到了几个有用的结果.

Using the same method used in paper , the properties of matrix characteristic equation which has pure imaginary eigenvalue, are analyzed, and the conditions under which homogenieus linear differential equation system with real coefficients has pure imaginary eigenvalue are further studied. Several useful results are gained.