摘要
通过给出实反对称矩阵正交标准形定理的新证明方法,进一步研究了实反对称矩阵正交标准形的一些应用。首先求出实反对称矩阵的中心化子及其维数,其次证明对每个正奇数m,实反对称矩阵只有一个m次实反对称矩阵根,最后从正交标准形出发直观地解答关于实反对称矩阵的一些基本结果。
In the report,a new proved method of the orthogonal canonical form theorem of real antisymmetric matrices was proposed,and some applications of the orthogonal canonical form of real antisymmetric matrices were further studied.Firstly,the centralizer and dimension of the real antisymmetric matrix were obtained;secondly,it was proved that for each positive odd number m,the real antisymmetric matrix has only one m-th root of real antisymmetric matrix;finally,some basic results about real antisymmetric matrices were intuitively solved from the orthogonal canonical form.
作者
张宸恩
赵静
刘合国
ZHANG Chenen;ZHAO Jing;LIU Heguo(School of Mathematics and Statistics,Hainan University,Haikou 570228,China)
基金
国家自然科学基金项目(12171142)。
