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# primitive matrix

A nonnegative square matrix $A=(a_{{ij}})$ is said to be a *primitive* matrix if there exists $k$ such that $A^{k}\gg 0$, i.e., if there exists $k$ such that for all $i,j$, the $(i,j)$ entry of $A^{k}$ is positive.

A sufficient condition for a matrix to be a primitive matrix is for the matrix to be a nonnegative, irreducible matrix with a positive element on the main diagonal.

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Reference

## Mathematics Subject Classification

15A51*no label found*15A48

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