Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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NONNEGATIVE INTEGRAL MATRICES HAVING GENERALIZED INVERSES

  • Kang, Kyung-Tae (Department of Mathematics Jeju National University) ;
  • Beasley, LeRoy B. (Department of Mathematics and Statistics Utah State University) ;
  • Encinas, Luis Hernandez (Department of Information Processing and Cryptography Institute of Physical and Information Technologies Spanish National Research Council) ;
  • Song, Seok-Zun (Department of Mathematics Jeju National University)
  • Received : 2013.09.23
  • Published : 2014.04.30
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Abstract

For an $m{\times}n$ nonnegative integral matrix A, a generalized inverse of A is an $n{\times}m$ nonnegative integral matrix G satisfying AGA = A. In this paper, we characterize nonnegative integral matrices having generalized inverses using the structure of nonnegative integral idempotent matrices. We also define a space decomposition of a nonnegative integral matrix, and prove that a nonnegative integral matrix has a generalized inverse if and only if it has a space decomposition. Using this decomposition, we characterize nonnegative integral matrices having reflexive generalized inverses. And we obtain conditions to have various types of generalized inverses.

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Acknowledgement

Supported by : National Research Foundation of Korea

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