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.
Highlights
There are many characterizations of linear operators from various matrix spaces into themselves which preserve term rank
We investigate the characterizations of linear maps which preserve term rank between different matrix spaces over anti-negative commutative semirings, which extends the previous results on characterizations of linear operators between different matrix spaces
We characterize the linear maps that preserve TR of p × q matrices over anti-negative commutative semirings, which are contained in Theorem 2
Summary
There are many characterizations of linear operators from various matrix spaces into themselves which preserve term rank. Boolean matrices, which preserve Boolean term rank. T preserves Boolean term rank if and only if it preserves Boolean term ranks 1 and 2;. T preserves Boolean term rank if and only if it doubly preserves Boolean term rank 1 or p. Beasley et al ([2]) characterized linear operators on the p × q matrices over a commutative anti-negative semiring which preserve term rank. The results are the following: For a linear operator on the p × q commutative anti-negative semiring matrices,. Song and Beasley([3]) characterized the linear maps that preserve term rank between different. We investigate the characterizations of linear maps which preserve term rank between different matrix spaces over anti-negative commutative semirings, which extends the previous results on characterizations of linear operators between different matrix spaces
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