On the exponent of a primitive matrix containing a primitive submatrix
A square matrix \(A\) of order \(n\) with nonnegative entries is said to be primitive if \(A^m\) has all positive entries for some \(m\geq 1\). The smallest such \(m\) is called the exponent of \(A\). For a primitive matrix of order \(n+k\) having a primitive submatrix of order \(n\), it is shown that the exponent of \(A\) is at most \((n- 1)^2+ 2k+1\).
scientific article; zbMATH DE number 1044254