P†-matrices: a generalization of P-matrices

被引:5
|
作者
Kannan, M. Rajesh [1 ]
Sivakumar, K. C. [1 ]
机构
[1] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India
来源
LINEAR & MULTILINEAR ALGEBRA | 2014年 / 62卷 / 01期
关键词
interval hull of matrices; P-dagger-matrix; Moore-Penrose inverse; P-#-matrix; group inverse; range kernel regularity; range-symmetric matrix; 15A09; PRINCIPAL MINORS; INVERSES; NONNEGATIVITY;
D O I
10.1080/03081087.2012.754438
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For A, B is an element of R-nxn, let r(A,B) (c(A,B)) be the set of matrices whose rows, (columns) are independent convex combinations of the rows (columns) of A and B. Johnson andTsatsomeros have shown that the set r(Lambda,B) (c(Lambda,B)) consists entirely of nonsingular matrices if and only if BA-1(B-1 A) is a P-matrix. For A, B is an element of R-nxn, let i (A, B) = {C is an element of R-nxn : min{a(i) (j), b(i) (j)} <= c(i) (j) <= max{a(i) (j), b(i) (j)}}. Rohn has shown that if all the matrices in i (A, B) are invertible, then BA(-1), A(-1)B, AB(-1) and B-1 A are P-matrices. In this article, we define a new class of matrices called P-dagger-matrices and present certain extensions of the above results to the singular case, where the usual inverse is replaced by the Moore-Penrose generalized inverse. The case of the group inverse is briefly discussed.
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页码:1 / 12
页数:12
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