Completely positive rank of some completely positive Boolean matrices
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An $n\times n$ Boolean matrix $A$ is called completely positive if it can be written as $BB^t$, where $B$ is an $n\times k$ Boolean matrix for some positive integer $k$. The smallest such $k$ is called the completely positive rank of $A$. In this article, we investigate the completely positive rank of $n\times n$ Boolean matrices. We compare completely positive rank with Boolean rank or column rank. We also determine the completely positive rank for some Boolean matrices of special types.
Abstract
An $n\times n$ Boolean matrix $A$ is called completely positive if it can be written as $BB^t$, where $B$ is an $n\times k$ Boolean matrix for some positive integer $k$. The smallest such $k$ is called the completely positive rank of $A$. In this article, we investigate the completely positive rank of $n\times n$ Boolean matrices. We compare completely positive rank with Boolean rank or column rank. We also determine the completely positive rank for some Boolean matrices of special types.