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

Kyung Tae Kang, Seok-Zun Song and Young Bae Jun
Additional contact information
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

Mathematics, 2020, vol. 8, issue 1, 1-8

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.

Keywords: matrix space; anti-negative semiring; term rank; linear map; ( P , Q , B )-block map (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/1/41/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/1/41/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:1:p:41-:d:304084

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().