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Open AccessArticle

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

1
Department of Mathematics, Jeju National University, Jeju 63243, Korea
2
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 41; https://doi.org/10.3390/math8010041
Received: 30 October 2019 / Revised: 19 December 2019 / Accepted: 20 December 2019 / Published: 1 January 2020
(This article belongs to the Special Issue Algebra and Discrete Mathematics)
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. View Full-Text
Keywords: matrix space; anti-negative semiring; term rank; linear map; (P, Q, B)-block map matrix space; anti-negative semiring; term rank; linear map; (P, Q, B)-block map
MDPI and ACS Style

Kang, K.T.; Song, S.-Z.; Jun, Y.B. Linear Maps that Preserve Any Two Term Ranks on Matrix Spaces over Anti-Negative Semirings. Mathematics 2020, 8, 41.

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