一类转置与自身的列向量组等价的特殊矩阵

A Class of Special Matrices with Equivalent Groups of Row and Transposed Column Vectors

先给出方阵的列向量组和行向量组的转置等价的充分必要条件.再对一类由初等矩阵诱导的列向量组和行向量组的转置等价的矩阵进行了研究,指出这一类特殊矩阵具有对称性和非平凡情况下的退化性.

First,the sufficient and necessary conditions for the equivalence of row vector groups and transposed column vector groups of square matrices are given.Secondly,a class of matrices of equivalent groups of row and transposed column vectors induced by elementary matrices are studied.It is pointed out that this special class of matrices are symmetric and degenerate in non-trivial cases.