RANK AND INERTIA OF SUBMATRICES OF THE MOORE-PENROSE INVERSE OF A HERMITIAN MATRIX

被引：0
作者：
Tian, Yongge [1 ]
机构：
[1] Cent Univ Finance & Econ, China Econ & Management Acad, Beijing 100081, Peoples R China
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2010年 / 20卷
关键词：
Hermitian matrix; Partitioned matrix; Moore-Penrose inverse; Rank; Inertia;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Closed-form formulas are derived for the rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix. A variety of consequences on the nonsingularity, nullity and definiteness of the submatrices are also presented.
引用
收藏
页码：226 / 240
页数：15
相关论文
共 21 条
[1]  
Ben-Israel A., 2003, Generalized inverses: theory and applications
[2]  
Bernstein D. S., 2009, MATRIX MATH THEORY F
[3]   COMPLETING A MATRIX WHEN CERTAIN ENTRIES OF ITS INVERSE ARE SPECIFIED [J].
FIEDLER, M ;
MARKHAM, TL .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1986, 74 :225-237
[4]   A NOTE ON MATRIX-INVERSION [J].
GUSTAFSON, WH .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1984, 57 (FEB) :71-73
[5]  
Haynsworth E. V., 1968, Linear Algebra Appl., V1, P299
[6]  
Haynsworth E. V., 1968, LINEAR ALGEBRA APPL, V1, P73, DOI [10.1016/0024-3795(68)90050-5, DOI 10.1016/0024-3795(68)90050-5]
[7]  
Hogben L., 2007, HDB LINEAR ALGEBRA
[8]  
Horn R.A., 2012, Matrix Analysis
[9]   MOORE-PENROSE INVERSE OF A PARTITIONED MATRIX M=(AD-BC) [J].
HUNG, C ;
MARKHAM, TL .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1975, 11 (01) :73-86
[10]  
Johnson C. R., 1992, OPER THEORY ADV APPL, V59, P234
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