Geodesic
Linear preserver of $n\times 1$ Ferrers vectors
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1189-1200
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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.
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.
DOI : 10.21136/CMJ.2023.0440-22
Classification : 05B20, 15A04
Keywords: Ferrers matrix; linear preserver; Boolean semiring 
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Fazlpar, Leila; Armandnejad, Ali. Linear preserver of $n\times 1$ Ferrers vectors. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1189-1200. doi: 10.21136/CMJ.2023.0440-22

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