任意体上矩阵完备为可逆阵问题

Problem on Complete to Invertible Matrix of Matrix over an Arbitrary Skew Field

由于可逆矩阵在矩阵论中的基本作用,因而对一矩阵添加适当子块,使之完备为可逆矩阵的问题是矩阵研究中的重要课题之一。对此。

On the basis of the papers [3] and [4], this paper proved the necessary and suffi- cient conditions of the completion problem of a matrix over an arbitrary skew field for the type are and gave the general solutions of the type (i), (ii).