M-matrix generalized inverses of M-matrices
نویسندگان
چکیده
منابع مشابه
Persistently positive inverses of perturbed M-matrices
A well known property of anM-matrixA is that the inverse is element-wise non-negative, which we write asA−1 0. In this paper we consider perturbations ofM-matrices and obtain bounds on the perturbations so that the non-negative inverse persists. The bounds are written in terms of decay estimates which characterize the decay (along rows) of the elements of the inverse matrix. We obtain results f...
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Recently, two distinct directions have been taken in an attempt to generalize the definition of an M-matrix. Even for nonsingular matrices, these two generalizations are not equivalent. The role of these and other classes of recently defined matrices is indicated showing their usefulness in various applications.
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We aim here at characterizing those nonnegative matrices whose inverse is an irreducible Stieltjes matrix. Specifically, we prove that any irreducible Stieltjes matrix is a resistive inverse. To do this we consider the network defined by the off-diagonal entries of the matrix and we identify the matrix with a positive definite Schrödinger operator which ground state is determined by the lowest ...
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Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of adL. For generic L a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The R-matrices are in general momentum dependent and dynamical. The constructi...
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In a recent paper Holtz showed that M–matrices satisfy Newton’s inequalities and so do the inverses of nonsingular M–matrices. Since nonsingular M–matrices and their inverses display various types of monotonic behavior, monotonicity properties adapted for Newton’s inequalities are examined for nonsingular M–matrices and their inverses. In the second part of the paper the problem of whether Draz...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)81117-2