• Corpus ID: 238634116

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… 

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