• DOI:10.1080/03081080500092380
• Corpus ID: 123043849

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}
}

• S. K. Neogy, A. K. Das
• Published 1 July 2005
• Mathematics
• Linear and Multilinear Algebra

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 et al. [Murthy, G.S.R., Parthasarathy, T. and Ravindran, G., 1993, A copositive Q-matrix which is not R 0. Mathematical Programming, 61, 131–135.] showed that Pang's conjecture ( ) is not true even when E 0 is replaced by C 0. We show that Pang's conjecture is true if E 0 is replaced by almost C 0 Finally, we present a game theoretic proof of necessary and sufficient conditions of an almost P 0-matrix satisfying Q-property.