Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A NOTE ON CONVERTIBLE {0,1} MATRICES

  • Kim, Si-Ju (Department of Mathematics Education, Andong University) ;
  • Park, Taeg-Young (Department of Mathematics Education, Andong University)
  • Published : 1997.10.01
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Abstract

A square matrix A with $per A \neq 0$ is called convertible if there exists a {1, -1} matrix H such that $per A = det(H \circ A)$ where $H \circ A$ denote the Hadamard product of H and A. In this paper, ranks of convertible {0, 1} matrices are investigated and the existence of maximal convertible matrices with its rank r for each integer r with $\left\lceil \frac{n}{2} \right\rceil \leq r \leq n$ is proved.

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References

  1. Applied Geometry and Discrete Mathematics v.4 On sign-nonsingular matrices and the conversion of the permanent into the determinant R. A. Brualdi;B. L. Shader
  2. Proc. Amer. Math. Soc. v.27 Conversion ot the permanent into the determinant P. M. Gibson
  3. Lin. Multilin. Alg. v.32 On convertible nonnegative matrices S. G. Hwang;S. J. Kim
  4. Lin. Multilin. Alg. v.38 On maximal convertible matrices S. G. Hwang;S. J. Kim;S. Z. Song
  5. Lin. Alg. Appl. v.233 On convertible complex matrices S. G. Hwang;S. J. Kim;S. Z. Song
  6. Bull. Korean. Math. Soc. v.29 Some remarks on extremal convertible matrices S. J. Kim