Perron-Frobenius theorem for nonnegative multilinear forms and extensions

Details Perron-Frobenius theorem for nonnegative multilinear forms and extensions Perron-Frobenius theorem for nonnegative multilinear forms and extensions

2009-05-11

arxiv.org/abs/0905.1626v3

Mathematics

Spectral Theory

13 pages

Scientific paper

10.1016/j.laa.2011.02.042

We prove an analog of Perron-Frobenius theorem for multilinear forms with
nonnegative coefficients, and more generally, for polynomial maps with
nonnegative coefficients. We determine the geometric convergence rate of the
power algorithm to the unique normalized eigenvector.

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