CAJ | 학술논문

通过刻画矩阵的初等因子对应的广义Jordan块的性质，在矩阵的初等因子组已知的前提下，给出了矩阵多项式秩的计算公式。作为结论的应用，考虑了当特征多项式和极小多项式相等时，矩阵多项式秩的情况。
통과각화구진적초등인자대응적엄의Jordan괴적성질，재구진적초등인자조이지적전제하，급출료구진다항식질적계산공식。작위결론적응용，고필료당특정다항식화겁소다항식상등시，구진다항식질적정황。
In this paper, we describe the properties of the blocks of the generalized Jordan corresponding to the elementary factor of matrix. By using the properties, we give the computational formula of the rank of polynomial of matrix under the condition that all elementary factors of the given matrix are known. As an application, we consider the situation of the rank of polynomial of matrix when the characteristic polynomial is equal to the minimal polynomial.