# Questions tagged [boolean-matrix]

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### Non-Orthogonal Vectors Problem

Consider the following problems: Orthogonal Vectors Problem Input: A set $S$ of $n$ Boolean vectors each of length $d$. Question: Do there exist distinct vectors $v_1$ and $v_2 \in S$ ...
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### Upper Bound on Number of $n \times n$ Boolean matrices of Boolean rank at most $k$

An $n \times n$ Boolean matrix $B$ has Boolean rank $k$ if there exist matrices $L \in \{0,1\}^{n \times k}$ and $R \in \{0,1\}^{k \times n}$, s.t. $B = L \circ R$. Here $\circ$ denotes the Boolean ...
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### Deciding transitivity of a directed acyclic graph [duplicate]

Is there any algorithm that decides whether a given directed acyclic graph is transitive or not, in time-complexity asymptotically better than boolean matrix multiplication?
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### What is the largest gap between rank and approximate rank?

We know that the log of the rank of a 0-1 matrix is the lower bound of deterministic communication complexity, and the log of the approximate rank is the lower bound of randomized communication ...
During my work i came up with the following problem: I am trying to find an $n \times n$ $(0,1)$-matrix $M$, for any $n > 3$, with the following properties: The determinant of $M$ is even. For ...