# On the computational equivalence of co-NP refutations of a matrix being a P-matrix

@article{Gordon2021OnTC, title={On the computational equivalence of co-NP refutations of a matrix being a P-matrix}, author={Spencer Gordon and Kevin Shu}, journal={ArXiv}, year={2021}, volume={abs/2110.05644} }

A P-matrix is a square matrix X such that all principal submatrices of X have positive determinant. Such matrices appear naturally in instances of the linear complementarity problem, where these are precisely the matrices for which the corresponding linear complementarity problem has a unique solution for any input vector. Testing whether or not a square matrix is a P-matrix is co-NP complete, so while it is possible to exhibit polynomiallysized witnesses for the fact that a matrix is not a P…

## References

SHOWING 1-7 OF 7 REFERENCES

The P-matrix problem is co-NP-complete

- Mathematics, Computer ScienceMath. Program.
- 1994

It is shown that given any matrix family belonging to the class of matrix polytopes with hypercube domains and rank-one perturbation matrices, a class which contains the intervalMatrices, testing singularity reduces to testing whether a certain matrix is not a P-matrix.

Digraph Models of Bard-Type Algorithms for the Linear Complementarity Problem

- Mathematics, Computer ScienceMath. Oper. Res.
- 1978

These digraphs show that such algorithms based on complementary pivoting for solving the linear complementarity problem can cycle even for symmetric, positive deFinite M, and provide some insight into the algorithms' behavior.

A partition theorem for Euclidean $n$-space

- Mathematics
- 1958

Let Vn be an n-dimensional vector space over the reals. Let s . . ' Sins 7)1, * * I, nbe 2n vectors in Vn such that every sequence of vectors { a,, , an }, where ai is either ti or vi, is a linearly…

Unique End of Potential Line

- MathematicsICALP
- 2019

UEOPL is shown to be a promise-subclass of EOPL in which the line in the End-of-Potential-Line instance is guaranteed to be unique via a promise, and OPDC lies in UEOPL, and the results imply that parity games, mean-payoff games, discounted games, and simple-stochastic games lie in UEopL.

Unique sink orientations of cubes

- MathematicsProceedings 2001 IEEE International Conference on Cluster Computing
- 2001

New algorithms are presented, a deterministic O(1.61/sup n/) procedure and a randomized O((43/20)/sup n/2/)=O( 1.47/Sup n%) procedure for unique sink orientations, which believe that unique sink orientation have a rich structure, and there is ample space for improvement on the bounds given above.

Theory of linear and integer programming

- MathematicsWiley-Interscience series in discrete mathematics and optimization
- 1999

Introduction and Preliminaries. Problems, Algorithms, and Complexity. LINEAR ALGEBRA. Linear Algebra and Complexity. LATTICES AND LINEAR DIOPHANTINE EQUATIONS. Theory of Lattices and Linear…