Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Sets of Integer Matrix Pairs Derived from Row Rank Inequalities and Their Preservers

  • Song, Seok-Zun (Department of Mathematics, Jeju National University) ;
  • Jun, Young-Bae (Department of Mathematics, Gyeongsang National University)
  • Received : 2011.06.17
  • Accepted : 2012.08.23
  • Published : 2013.06.23
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Abstract

In this paper, we consider the row rank inequalities derived from comparisons of the row ranks of the additions and multiplications of nonnegative integer matrices and construct the sets of nonnegative integer matrix pairs which is occurred at the extreme cases for the row rank inequalities. We characterize the linear operators that preserve these extreme sets of nonnegative integer matrix pairs.

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References

  1. L. B. Beasley, A. E. Guterman, Rank inequalities over semirings, Journal of the Korean Math. Soc., 42(2)(2005), 223-241. https://doi.org/10.4134/JKMS.2005.42.2.223
  2. L. B. Beasley, A. E. Guterman, Linear preservers of extremes of rank inequalities over semirings, Factor rank, Journal of Mathematical Sciences (New York), 131(2005), 5919-5938. https://doi.org/10.1007/s10958-005-0451-1
  3. L. B. Beasley, A. E. Guterman, C. L. Neal, Linear preservers for Sylvester and Frobe-nius bounds on matrix rank, Rocky Mountains J. of Mathematics, 36(1)(2006), 67-80. https://doi.org/10.1216/rmjm/1181069488
  4. L. B. Beasley, S.-G. Lee, S.-Z. Song, Linear operators that preserve pairs of matrices which satisfy extreme rank properties, Linear Algebra Appl., 350(2002), 263-272. https://doi.org/10.1016/S0024-3795(02)00293-8
  5. L. B. Beasley, S. Z. Song, K. T. Kang and B. K. Sarma, Column ranks and their preservers over nonnegative real matrices, Linear Algebra Appl. 399(2005), 3-16. https://doi.org/10.1016/j.laa.2004.04.022
  6. P. Pierce and others, A Survey of Linear Preserver Problems, Linear and Multilinear Algebra, 33(1992), 1-119. https://doi.org/10.1080/03081089208818176