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

作　　者：侯汝臣[1] 李波[1] HOU Ruchen;LI Bo(School of Mathematics and Information Science,Yantai University,Yantai Shandong 264005,China)

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《大学数学》2024年第5期48-50,共3页College Mathematics

基　　金：山东省自然科学基金(ZR2021MA015);中国高等教育学会高等教育科学研究规划课题(23SX0312);烟台大学教学改革研究项目(jyxm2021049)。

摘　　要：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.

关 键 词：对称矩阵 反对称矩阵 行向量组 列向量组 等价 

分 类 号：O151.21[理学—数学]