Abstract
The Perron complement is a smaller matrix derived in a natural way from a square nonnegative matrix. By compressing the directed graph of a nonnegative matrix in a certain way, we analyze fully the connected components, irreducibility and primitivity of its Perron complement with respect to a given subset of indices.
This work supported in part by National Science Foundation grant DMS 92–00899 and by Office of Naval Research contract N00014–90-J-1739.
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References
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© 1993 Springer-Verlag New York, Inc.
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Johnson, C.R., Xenophontos, C. (1993). Irreducibility and Primitivity of Perron Complements: Application of the Compressed Directed Graph . In: George, A., Gilbert, J.R., Liu, J.W.H. (eds) Graph Theory and Sparse Matrix Computation. The IMA Volumes in Mathematics and its Applications, vol 56. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8369-7_5
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DOI: https://doi.org/10.1007/978-1-4613-8369-7_5
Publisher Name: Springer, New York, NY
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