摘要
利用外逆的性质及矩阵方程MFX+YEM=M有解的充分和必要条件,研究了同一个矩阵A的若干个外逆的秩,得出了矩阵A的若干个外逆的一些秩等式,这些秩等式推广了TianY和Styan G P H(when does rank(ABC)=rank(AB)+rank(BC)-rank(B)hold·Internat J Math EDSci.Technol,2002,33:127～137.)的结果.
By using the properties of outer inverses of matrix and the necessary and sufficient condition of the solution of the matrix equation MFX＋ YEM =N,the ranks of some outer inverses of the same matrix A is researched and some rank equalities of outer inverses of the matrix A is obtained ,which generalized the results of Tian Y and Styan G P H（ when does rank （ABC） = rank（AB） ＋ rank（Be） - rank（ B） hold？ Internat J Math ED Sci. Technol,2002,33：127 - 137. ）.
出处
《湖北师范学院学报（自然科学版）》
2009年第2期1-5,共5页
Journal of Hubei Normal University(Natural Science)
关键词
矩阵的外逆
矩阵的广义逆
矩阵的秩
幂等阵
outer inverse of a matrix
generalize inverse of a matrix
rank of a matrix
idempotent matrix
