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Linear Maps that Preserve Any Two Term Ranks on Matrix Spaces over Anti-Negative Semirings

Author

Listed:
  • Kyung Tae Kang

    (Department of Mathematics, Jeju National University, Jeju 63243, Korea)

  • Seok-Zun Song

    (Department of Mathematics, Jeju National University, Jeju 63243, Korea)

  • Young Bae Jun

    (Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea)

Abstract

There are many characterizations of linear operators from various matrix spaces into themselves which preserve term rank. In this research, we characterize the linear maps which preserve any two term ranks between different matrix spaces over anti-negative semirings, which extends the previous results on characterizations of linear operators from some matrix spaces into themselves. That is, a linear map T from p × q matrix spaces into m × n matrix spaces preserves any two term ranks if and only if T preserves all term ranks if and only if T is a ( P , Q , B )-block map.

Suggested Citation

  • Kyung Tae Kang & Seok-Zun Song & Young Bae Jun, 2020. "Linear Maps that Preserve Any Two Term Ranks on Matrix Spaces over Anti-Negative Semirings," Mathematics, MDPI, vol. 8(1), pages 1-8, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:41-:d:304084
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