Multi-dimensional nonlinear Perron-Frobenius theorem and some applications

Dr. Francesco Tudisco ( Department of Mathematics and Statistics, University of Strathclyde)

Frank Adams 1,

The nonlinear Perron-Frobenius theory addresses existence,  uniqueness and maximality of positive eigenpairs for order-preserving homogeneous functions. 
This is an important and relatively recent generalization of the famous result for nonnegative matrices.  In this
talk I present a further generalization of this theory to ''multi-dimensional'' order-preserving and homogeneous maps, which we briefly call multi-homogeneous maps.  The results presented are then used to discuss some nonlinear matrix and tensor eigenvalue problems and a new eigenvector-based centrality measure for nodes and layers of multi-layer networks.

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