A Note on Covertible $\{0, 1\}$ Matrices
Commun. Korean Math. Soc. 1997 Vol. 12, No. 4, 841-849
Si-Ju Kim, Taeg-Young Choi
Andong university, Andong university
Abstract : A square matrix $A$ with $perA \not= 0$ is called convertible if there exists a $\{1,-1\}$ matrix $H$ such that $perA=det(H\circ A)$ where $H\circ A$ denote the Hadamard product of $H$ and $A$. In this paper, ranks of convertible $\{0,1\}$ matrices are investigated and the existence of maximal convertible matrices with its rank $r$ for each integer $r$ with $\lceil {n\over 2}\rceil\le r \le n$ is proved.
Keywords : convertible, rank, permanents
MSC numbers : 53C25
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