# On almost type classes of matrices with Q-property

@article{Neogy2005OnAT, title={On almost type classes of matrices with Q-property}, author={S. K. Neogy and A. K. Das}, journal={Linear and Multilinear Algebra}, year={2005}, volume={53}, pages={243 - 257} }

In this article, we introduce a new matrix class almost (a subclass of almost N 0-matrices which are obtained as a limit of a sequence of almost N-matrices) and obtain a sufficient condition for this class to hold Q-property. We produce a counter example to show that an almost -matrix need not be a R 0-matrix. We also introduce another two new limiting matrix classes, namely of exact order 2, for a positive vector d and prove sufficient conditions for these classes to satisfy Q-property. Murthy…

## 17 Citations

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## References

SHOWING 1-10 OF 22 REFERENCES

Some Properties of Fully Semimonotone, Q0-Matrices

- MathematicsSIAM J. Matrix Anal. Appl.
- 1995

It is shown that the conjecture that the same must be true for fully semimonotone ($E^{f}_{0}$) matrices is true for matrices of order up to $4 \times 4$ and partially resolve it for higher order matrices.

A copositive Q-matrix which is notR0

- MathematicsMath. Program.
- 1993

This note presents an example of a copositive Q-matrix which is notR0, based on the following elementary proposition: LetA be a square matrix of ordern.

AlmostP0-matrices and the classQ

- Mathematics, EconomicsMath. Program.
- 1992

This paper demonstrates that within the class of thosen × n real matrices, each of which has a negative determinant, nonnegative proper principal minors and inverse with at least one positive entry,…

Some classes of matrices in linear complementarity theory

- MathematicsMath. Program.
- 1973

A class of matrices is introduced such that for anyM in this class a solution to the linear complementarity problem exists for all feasibleq, and such that Lemke's algorithm will yield a solution or demonstrate infeasibility.

A Characterization of the Constant Parity Property of the Number of Solutions to the Linear Complementarity Problem

- Mathematics
- 1972

We consider the linear complementarily problem: Given an $m \times m$ matrix M and a real m-vector q, find real m-vectors x and y which solve (i) $x = My + q,x\geqq 0,y\geqq 0$, (ii) $x^T y = 0$. In…

On co-positive, semi-monotoneQ-matrices

- MathematicsMath. Program.
- 1995

In this paper we consider not necessarily symmetric co-positive as well as semi-monotoneQ-matrices and give a set of sufficient conditions for such matrices to beR0-matrices. We give several examples…

The Linear Complementarity Problem with Exact Order Matrices

- MathematicsMath. Oper. Res.
- 1994

A complete characterization of the class of exact order 1 based on the number of solutions to the LCPq, A for each q ∈ Rn is presented.