Abstract
In this paper various properties of fully indecomposable matrices are investigated. Several integer-valued functions of nonnegative matrices are defined and various relations between them are obtained and, where appropriate, related to corresponding concepts in graph theory. These relations are used to obtain upper bounds on the index of primitivity of a fully indecomposable matrix. Matrix and Kronecker products of fully indecomposable matrices are considered, and lastly the connection between fully indecomposable matrices and essentially nonsingular matrices is examined.
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