n×n阶矩阵的度量

Metric of n×n-Order Matrix and Application

利用矩阵迹给出n×n阶矩阵的内积、范数和度量,利用度量给出矩阵上的点、矩阵空间之间的一些距离关系;讨论了点到上三角矩阵及上三角可逆阵的距离公式.

In this paper, by using trace of n×n- order matrix, we define a norm on n×n-order matrix. And then we define the base length, distance, the distance between the point and space. As an application, we obtain distance formula between point on n×n-order matrix and upper triangular matrix, point on n×n- order matrix and invertible upper triangular matrix.