Geodesic
On the derivatives of the Perron vector
Portugaliae mathematica, Tome 43 (1985) no. 1, pp. 35-42.

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Keywords: second order partial derivatives of the Perron root, nonnegative, and irreducible matrix, group inverse, M-matrix, Perron vector 
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     author = {Deutsch, Emeric and Neumann, Michael},
     title = {On the derivatives of the {Perron} vector},
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     zbl = {0594.15008},
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Deutsch, Emeric; Neumann, Michael. On the derivatives of the Perron vector. Portugaliae mathematica, Tome 43 (1985) no. 1, pp. 35-42. http://geodesic.mathdoc.fr/item/PORMA_1985__43_1_114537/