Perron-Frobenius theorem for nonnegative multilinear forms and extensions
arXiv:0905.1626388 citations
Originality Incremental advance
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Provides a foundational theoretical result for multilinear algebra and tensor analysis, with potential impact on optimization and spectral theory.
The paper extends the Perron-Frobenius theorem to nonnegative multilinear forms and polynomial maps, proving existence and uniqueness of a normalized eigenvector and determining the geometric convergence rate of the power algorithm.
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.