EQUIVALENT CONDITIONS FOR THE REVERSE ORDER PROPERTY INVARIANCE UNDER GENERALIZED INVERSES OF MATRICES

被引：0

作者：

Zekraoui, Hanifa ^{[1
]}

Guedjiba, Said ^{[2
]}

机构：

[1] LArbi Ben MHidi Univ, Fac Sci, Dept Math, Oum El Bouaghi 04000, Algeria

[2] Batna Univ, Fac Sci, Dept Math, Batna 05000, Algeria

来源：

ICMS: INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCE | 2010年 / 1309卷

关键词：

Generalized Inverse; Reverse Order; Rank; Range; PRODUCT;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The property of "reverse order law" related to generalized inverses of a matrix product AB, is the property (AB)(-) = B- A(-) for some A(-), B- and (AB)(-) generalized inverses of A, B and AB respectively. When this property holds for all generalized inverses of them, which means that it is invariant under generalized inverses, we call this "reverse order property invariance". In this paper we will investigate certain invariance properties of the product AB(-)C for studing some equivalent conditions for the reverse order property invariance. The references of Y. Tian will be the basic idea of the proofs throughout the paper.

引用

页码：927 / +

页数：3

共 8 条

[1]

Bapat RB., 2000, Linear Algebra and Linear Models, V2

[2]

Ben-Israel A., 2003, Generalized inverses: theory and applications

[3] NOTE ON GENERALIZED INVERSE OF PRODUCT OF MATRICES [J].

CLINE, RE .

SIAM REVIEW, 1964, 6 (01) :57-&

[4]

Erdelyi I., 1966, J ASSOC COMPUT MACH, V13, P493

[5] NOTE ON FITTING OF FUNCTIONS OF SEVERAL INDEPENDENT VARIABLES [J].

GREVILLE, TNE .

JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1961, 9 (01) :109-115

[6] Invariance properties of a triple matrix product involving generalized inverses [J].

Gross, Juergen ;

Tian, Yongge .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 417 (01) :94-107

[7]

Ren X. M., 2005, PURE MATH APPL, V16, P191

[8]

Tian Y., 2003, New York J. Math., V9, P345

← 1 →