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Separability of distinct Boolean rank-1 matrices

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Abstract

For two distinct rank-1 matricesA andB, a rank-1 matrixC is called aseparating matrix ofA andB if the rank ofA+C is 2 but the rank ofB+C is 1 or vice versa. In this case, rank-1 matricesA andB are said to beseparable. We show that every pair of distinct Boolean rank-1 matrices are separable.

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Author information

Correspondence to Seok-Zun Song.

Additional information

Seok-Zun Song received his Doctor of Science at Kyungpook National University. Since 1983 he has been at the Cheju National University. His research interests center on the linear preserver problems.

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Song, S. Separability of distinct Boolean rank-1 matrices. JAMC 18, 197–204 (2005). https://doi.org/10.1007/BF02936565

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AMS Mathematics Subject Classification

  • 15A23
  • 15A03

Key words and phrases

  • Boolean matrix
  • separable matrix
  • perimeter