# primitive matrix

A nonnegative square matrix $A=(a_{ij})$ is said to be a 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.

Title primitive matrix PrimitiveMatrix 2013-03-22 13:18:18 2013-03-22 13:18:18 Mathprof (13753) Mathprof (13753) 12 Mathprof (13753) Definition msc 15A51 msc 15A48