Generalized ultrametric matrices — a class of inverse M-matrices

@article{Nabben1995GeneralizedUM,
  title={Generalized ultrametric matrices — a class of inverse M-matrices},
  author={Reinhard Nabben and Richard S. Varga},
  journal={Linear Algebra and its Applications},
  year={1995},
  volume={220},
  pages={365-390}
}
  • R. Nabben, R. Varga
  • Published 15 April 1995
  • Mathematics
  • Linear Algebra and its Applications
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  • Mathematics
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  • 2001
TLDR
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It is well known that every $n \times n$ Stieltjes matrix has an inverse that is an $n \times n$ nonsingular symmetric matrix with nonnegative entries, and it is also easily seen that the converse of
On the inverse M-matrix problem for real symmetric positive-definite Toeplitz matrices
Necessary and sufficient conditions are obtained for a real symmetric positive-definite Toeplitz matrix R to be an inverse of an M-matrix in terms of its Schur coefficients. Related problems are also
Inverse of Strictly Ultrametric Matrices are of Stieltjes Type
This paper shows that a nonnegative ultrametric matrix $A$ is nonsingular and that its inverse is a strictly diagonally dominant Stieltjes matrix. The method consists of studying the spectral
Nonnegative matrices whose inverses are M-matrices
A characterization of a class of totally nonnegative matrices whose inverses are M-matrices is given. It is then shown that if A is nonnegative of order n and A-1 is an M-matrix, then the almost
Matrix computations
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