Perron–Frobenius theorem for nonnegative multilinear forms and extensions

作者: S. Friedland , S. Gaubert , L. Han

DOI: 10.1016/J.LAA.2011.02.042

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摘要: … We prove an analog of Perron–Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We …

参考文章(11)
Stéphane Gaubert, Jeremy Gunawardena, The Perron-Frobenius theorem for homogeneous, monotone functions Transactions of the American Mathematical Society. ,vol. 356, pp. 4931- 4950 ,(2004) , 10.1090/S0002-9947-04-03470-1
MARIANNE AKIAN, STÉPHANE GAUBERT, ALEXANDER GUTERMAN, TROPICAL POLYHEDRA ARE EQUIVALENT TO MEAN PAYOFF GAMES International Journal of Algebra and Computation. ,vol. 22, pp. 1250001- ,(2012) , 10.1142/S0218196711006674
K. C. Chang, K. Pearson, T. Zhang, Perron-Frobenius theorem for nonnegative tensors Communications in Mathematical Sciences. ,vol. 6, pp. 507- 520 ,(2008) , 10.4310/CMS.2008.V6.N2.A12
Michael Ng, Liqun Qi, Guanglu Zhou, Finding the Largest Eigenvalue of a Nonnegative Tensor SIAM Journal on Matrix Analysis and Applications. ,vol. 31, pp. 1090- 1099 ,(2009) , 10.1137/09074838X
Roger D. Nussbaum, Convexity and log convexity for the spectral radius Linear Algebra and its Applications. ,vol. 73, pp. 59- 122 ,(1986) , 10.1016/0024-3795(86)90233-8
Liqun Qi, Eigenvalues of a real supersymmetric tensor Journal of Symbolic Computation. ,vol. 40, pp. 1302- 1324 ,(2005) , 10.1016/J.JSC.2005.05.007
Lek-Heng Lim, Singular values and eigenvalues of tensors: a variational approach ieee international workshop on computational advances in multi-sensor adaptive processing. pp. 129- 132 ,(2005) , 10.1109/CAMAP.2005.1574201
Shmuel Friedland, Convergence of products of matrices in projective spaces Linear Algebra and its Applications. ,vol. 413, pp. 247- 263 ,(2006) , 10.1016/J.LAA.2004.06.021
Andrew D. Burbanks, Roger D. Nussbaum, Colin T. Sparrow, Extension of order-preserving maps on a cone Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 133, pp. 35- 59 ,(2003) , 10.1017/S0308210500002274