选主元矩阵原位替换解算方法

矩阵行列式、矩阵方程未知数和矩阵逆阵元素,可采用矩阵原位替换解算方法,利用矩阵元素约化值进行解算,但矩阵元素约化值计算过程中要求矩阵主元约化值不能等于零,在没有确认矩阵是否满秩的情况下,其值等于零有可能由矩阵元素排列结构引起,也有可能由矩阵秩亏引起,如何判别矩阵主元约化值为零的成因,在排除矩阵秩亏的情况下,如何利用选主元矩阵原位替换解算方法继续完成相应矩阵解算,是本文研究的内容。该研究可使矩阵原位替换解算方法得到更加广泛的应用。

The in-situ replacement calculation method of choosing principle component matrix

Matrix determinant,matrix equation unknown element and inverse matrix element can be calculated by matrix element reduction using matrix in-situ replacement calculation method.But the matrix principle component reduction can not be zero during the process of matrix element reduction calculation.When it doesn't confirm the matrix is full rank or not,the arrangement structure of matrix element may cause its value being zero,or the matrix low rank may cause that.How to differentiate the reason of matrix principle component zero value? When excluding the matrix low rank,how to use the in-situ replacement calculation method of choosing principle component matrix to continue calculate the according matrix? That is studied in this paper.And the study will spread the application of the matrix in-situ calculation method.