Hidden Z-matrices with positive principal minors☆

@article{Pang1979HiddenZW,
  title={Hidden Z-matrices with positive principal minors☆},
  author={J. S. Pang},
  journal={Linear Algebra and its Applications},
  year={1979},
  volume={23},
  pages={201-215}
}
  • J. Pang
  • Published 1 February 1979
  • Mathematics
  • Linear Algebra and its Applications
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47 Citations
Highly Influential Citations
8
Background Citations
15
Methods Citations
3

47 Citations

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Citation Type

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Generalizations of the hidden Minkowski property
On Some Properties of $K$- type Block Matrices in the context of Complementarity Problem
TLDR
The solution of linear complementarity problem with K-type block matrices can be obtained by solving a linear programming problem and it is shown that block triangular K-matrices satisfy least element property.
M-matrix and inverse M-matrix extensions
Abstract A class of matrices that simultaneously generalizes the M-matrices and the inverse M-matrices is brought forward and its properties are reviewed. It is interesting to see how this class…
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References

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Abstract : The purpose of this survey is to classify systematically a widely ranging list of characterizations of nonsingular M-matrices from the economics and mathematics literatures. These…
M-matrix characterizations.I—nonsingular M-matrices
A linear complementarity problem with an n by 2n “P”-matrix
The problem considered in this paper is given by the conditions: w=q+Mv+Nx, w≧0, v≧0, x≧0, v≦r, w T v=0 and (r−v) T x=0. Here q, r are n-vectors with r>0 and M, N are n by n matrices. We say that an…
On the simplex method and a class of linear complementary problems
A note on an open problem in linear complementarity
  • J. Pang
  • Mathematics
    Math. Program.
  • 1977
TLDR
This note proves a result which improves on a characterization obtained by Mangasarian of the class ofn × n matricesM such that for everyn-vectorq for which the linear complementarity problem (q, M) is feasible, then the problem has a solution.
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…
On a class of least-element complementarity problems
  • J. Pang
  • Mathematics
    Math. Program.
  • 1979
TLDR
Two least-element characterizations of solutions to the above linear complementarity problem are established and a new and direct method to solve this class of problems, which depends on the idea of “least-element solution” is presented.
Isotone Solutions of the Parametric Complementarity Problems.
TLDR
This paper studies the behavior of solutions to the parametric complementarity problem as the parameter alpha increases from zero.
Characterization of linear complementarity problems as linear programs
It is shown that the linear complementarity problem of finding an n-by-1 vector x such that Mx+q≧0, x≧0, and x T(Mx+q)=0, where M is a given n-by-n real matrix and q is a given n-by-1 vector, is…
On Cone Orderings and the Linear Complementarity Problem.
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