关于满秩矩阵集合的两个性质  

On two properties of the set of full rank matrices

作　　者：郑华[1] 

机构地区：[1]韶关学院数学系,广东韶关512005

出　　处：《韶关学院学报》2008年第9期6-8,共3页Journal of Shaoguan University

摘　　要：利用矩阵的奇异值分解理论,证明满秩矩阵集合是开集,并且是稠密的,进而说明了矩阵元素的扰动对矩阵秩的影响,以及满秩矩阵集合与秩亏矩阵集合的关系.The set of full rank matrices is proved to be open and dense, using the theory of singular value decomposition. The effect of the rank of a matrix by disturbance of its items is explained, and a relationship between the set of full rank matrices and the set of rank deficiency matrices is showed.

关 键 词：奇异值分解 满秩矩阵 秩亏矩阵 

分 类 号：O151.21[理学—数学]