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Sorry if this is a simple question, but I'm unsure about what this notation means. Here is the statement I am confused about:

The Perron-Frobenius Theorem: Let $A$ be an indecomposable nonnegative matrix with $\rho(A) = 1$. Denote by $r$ the minimal rank of nonzero members of $\overline{\mathbb{R^+}S}$, where $S$ is the semigroup generated by $A$.

It goes on to explain the theorem but I am confused about the notation $\overline{\mathbb{R^+}S}$. Could someone explain what it means in this context? Thanks in advance

Edit: I know that ${\mathbb{R^+}S}$ is the set $\{cA| c \in \mathbb{R^+}, A \in S\}$, but I am specifically asking about $\overline{\mathbb{R^+}S}$ and how it is different from ${\mathbb{R^+}S}$

Smeef
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  • That overline usually means closure, so I'll guess that $\overline{\mathbb{R^+}S}$ means the closure of $\mathbb{R^+}S$ in the space of matrices. – Lee Mosher Jul 11 '17 at 18:07
  • @LeeMosher I see, that makes sense now. Thank you very much – Smeef Jul 11 '17 at 18:13

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