摘要
设Ｍ＝ＡＢＣＤ为复数域上的矩阵，其中Ａ为ｍ×ｎ矩阵，ｒａｎｋＡ＝ｒ≤ｍｉｎ（ｍ，ｎ），Ｂ为ｍ×ｒ１矩阵，ｒａｎｋＢ＝ｒ１，Ｃ为ｒ２×ｎ矩阵，ｒａｎｋＣ＝ｒ２，ｍ＋ｒ２＝ｎ＋ｒ１．本文研究了矩阵Ｍ的奇异性，给出了Ｍ为非奇异矩阵的充分必要条件，也给出了Ｍ－１＝Ａ＋Ｃ＋Ｂ＋Ｄ＋的充分必要条件．
Let M=A B C D,where A is a m×n matrix with rank r≤min (m,n),B is a m×r 1matrix with rank r 1 and C is a r 2×n matrix with rank r 2,m+r 2=n+r 1.In this paper,we give the necessary and sufficient conditions for nonsigularity of M.Besides, we also give the necessary and sufficient Conditions for M -1 =A + C + B + D +.
出处
《宝鸡文理学院学报（自然科学版）》
CAS
1999年第1期6-11,共6页
Journal of Baoji University of Arts and Sciences(Natural Science Edition)
关键词
分块矩阵
非奇异矩阵
奇异性
充要条件
矩阵
Partitioned matrix
Nonsingular matrix
Necessary and sufficient conditions
