# Properties of some matrix classes based on principal pivot transform

@article{Das2016PropertiesOS, title={Properties of some matrix classes based on principal pivot transform}, author={A. K. Das}, journal={Annals of Operations Research}, year={2016}, volume={243}, pages={375-382} }

In this article, we study the properties of some matrix classes using principal pivot transform (PPT). These matrices with some additional conditions have nonnegative principal minors. We show that a subclass of almost fully copositive matrices intorduced in (Linear Algebra Appl 400:243–252 2005) with $$Q_{0}$$Q0-property is captured by sufficient matrices introduced by Cottle et al. in (Linear Algebra Appl 114/115:231–249 1989) and the solution set of a linear complementarity problem is the…

## 12 Citations

Ju l 2 01 9 On Semimonotone Star Matrices and Linear Complementarity Problem

- Mathematics
- 2019

In this article, we introduce the class of semimonotone star (E 0) matrices. We establish the importance of E 0-matrix in the context of complementarity theory. We illustrate that the principal pivot…

On Some Properties of $K$- type Block Matrices in the context of Complementarity Problem

- Mathematics, Computer Science
- 2021

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.

On semimonotone star matrices and linear complementarity problem

- MathematicsOperators and Matrices
- 2021

In this article, we introduce the class of semimonotone star ($E_0^s$) matrices. We establish the importance of the class of $E_0^s$-matrices in the context of complementarity theory. We show that…

On Column Competent Matrices and Linear Complementarity Problem

- MathematicsICMC
- 2021

Abstract We revisit the class of column competent matrices and study some matrix theoretic properties of this class. The local w-uniqueness of the solutions to the linear complementarity problem can…

On Linear Complementarity Problem with Hidden Z-Matrix

- Mathematics
- 2018

In this article we study linear complementarity problem with hidden Z-matrix. We extend the results of Fiedler and Pták for the linear system in complementarity problem using game theoretic approach.…

More on hidden Z-matrices and linear complementarity problem

- Mathematics, Computer ScienceLinear and Multilinear Algebra
- 2019

It is shown that for a non-degenerate feasible basis, linear complementarity problem with hidden Z-matrix has unique non- Degenerate solution under some assumptions.

On some properties of $\omega$-uniqueness in tensor complementarity problem

- Mathematics
- 2022

In this article we introduce column adequate tensor in the context of tensor complementarity problem and consider some important properties. The tensor complementarity problem is a class of nonlinear…

O C ] 3 0 M ay 2 01 9 More On Hidden Z-Matrices and Linear Complementarity Problem

- Mathematics
- 2019

In this article we study linear complementarity problem with hidden Z-matrix. We extend the results of Fiedler and Pták for the linear system in complementarity problem using game theoretic approach.…

Bounded Homotopy Path Approach to Find the Solution of Linear Complementarity Problems

- Mathematics
- 2021

In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the Linear Complementarity Problem. Earlier…

Solution of Tensor Complementarity Problem Using Homotopy Function

- Mathematics
- 2022

The paper aims to propose a suitable method in ﬁnding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which…

## References

SHOWING 1-10 OF 22 REFERENCES

On almost type classes of matrices with Q-property

- Mathematics
- 2005

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…

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,…

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.

OnQ-matrices

- MathematicsMath. Program.
- 1979

It is shown that the same characterization holds for anL-matrix as well, and that the symmetricCopositive-plusQ-matrices are precisely those which are strictly copositive.