Eventually cyclic matrices and a test for strong eventual nonnegativity
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Eventually r-cyclic matrices are deﬁned, and it is shown that if A is an eventually r-cyclic matrix A having rank A2 = rank A, then A is r-cyclic with the same cyclic structure. This result and known Perron-Frobenius theory of eventually nonnegative matrices are used to establish an algorithm to determine whether a matrix is strongly eventually nonnegative (i.e., is an eventually nonnegative matrix having a power that is both irreducible and nonnegative).
This article is published as Hogben, Leslie. "Eventually cyclic matrices and a test for strong eventual nonnegativity." The Electronic Journal of Linear Algebra 19 (2010): 129-140. DOI: 10.13001/1081-3810.1353. Posted with permission.