East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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ON SIGNED SPACES

  • Kim, Si-Ju (Department of Mathematics Education Andong National University) ;
  • Choi, Taeg-Young (Department of Mathematics Education Andong National University)
  • Received : 2010.09.19
  • Accepted : 2011.01.06
  • Published : 2011.01.31
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Abstract

We denote by $\mathcal{Q}(A)$ the set of all matrices with the same sign pattern as A. A matrix A has signed -space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the -space of e $\tilde{A}$ is S, for each e $\tilde{A}{\in}\mathcal{Q}(A)$. In this paper, we show that the number of sign patterns of elements in the row space of $\mathcal{S}^*$-matrix is $3^{m+1}-2^{m+2}+2$. Also the number of sign patterns of vectors in the -space of a totally L-matrix is obtained.

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References

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