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

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
• (<i>p</i>, <i>q</i>, <i>b</i>)-block map