منابع مشابه
-weighted Group Inverses
Nonnegative rectangular matrices having nonnegative Unweighted group inverses are characterized. Our techniques suggest an interesting approach to extend the earlier known results on X-monotone square matrices to rectangular ones. We also answer a question of characterizing nonnegative matrices having a nonnegative solution Y where (1) A = AXA, (2) X = XAX, (3) (AX) is O-symmetric, (4) ( XA) is...
متن کاملOn Nonnegative Moore-Penrose Inverses of Perturbed Matrices
We consider the problem of characterizing nonnegativity of the Moore-Penrose inverse for matrix perturbations of the type A − XGY, when the Moore-Penrose inverse of A is nonnegative. Here, we say that a matrix B = (b ij ) is nonnegative and denote it by B ≥ 0 if b ij ≥ 0, ∀i, j. This problemwasmotivated by the results in [1], where the authors consider an M-matrix A and find sufficient conditio...
متن کاملGroup Inverses and Drazin Inverses over Banach Algebras
For a matrix over a complex commutative unital Banach algebra, necessary and suucient conditions are given for the existence of its group inverse, and more generally, its Drazin inverses. The conditions are easy to check and explicit formulas for the inverses are provided. Some properties of the inverses and an application to operator theory are discussed. This note is a continuation of an earl...
متن کاملOn Splittings of Matrices and Nonnegative Generalized Inverses
The authors introduce a new type of matrix splitting generalizing the notion of B splitting and study its relationships with nonnegativity of the Moore-Penrose inverse and the group inverse. Mathematics subject classification (2010): 15A09, 15B48.
متن کاملGroup inverses of matrices with path graphs
A simple formula for the group inverse of a 2× 2 block matrix with a bipartite digraph is given in terms of the block matrices. This formula is used to give a graph-theoretic description of the group inverse of an irreducible tridiagonal matrix of odd order with zero diagonal (which is singular). Relations between the zero/nonzero structures of the group inverse and the Moore-Penrose inverse of...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1991
ISSN: 0024-3795
DOI: 10.1016/0024-3795(91)90355-z