一类三阶非对称实矩阵合同的充要条件

A Necessary and Sufficient Condition on the Congruence of Non-symmetric Real Matrices

从两个非对称实矩阵合同的定义出发,给出了两个二阶非对称实矩阵合同的判定条件.利用矩阵的计算技巧和待定系数法,将一类三阶非对称实矩阵合同的判定归结于二阶非对称实矩阵的情形,并刻画了两类非对称实矩阵合同的等价关系,最后得出了一类三阶非对称实矩阵合同判定的一个充要条件.

Within the knowledge of linear algebra courses,starting from the definition of the congruence of non-asymmetric real matrices,we give the conditions for judging the congruence of two 2×2 non-asymmetric real matrices.Based on the calculation technique of matrix and the method of undetermined coefficient,the judgment of the congruence of a class of 3×3 non-asymmetric real matrices come down to the case of 2×2 non-asymmetric real matrices,and the equivalence relation about the congruence between the two classes of non-asymmetric real matrices is described.Finally,a necessary and sufficient condition on the congruence of 3×3non-symmetric real matrices is given.