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Keywords:
Ferrers matrix; linear preserver; Boolean semiring
Ferrers matrix; linear preserver; Boolean semiring
Summary:
Let $A=[a_{ij}]_{m\times n}$ be an $m\times n$ matrix of zeros and ones. The matrix $A$ is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero $(1,1)$-entry. We characterize all linear maps perserving the set of $n\times 1$ Ferrers vectors over the binary Boolean semiring and over the Boolean ring $\mathbb {Z}_2$. Also, we have achieved the number of these linear maps in each case.
References:
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