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Perron–Frobenius theorem for nonnegative multilinear forms and extensions
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 geometricExpand
Dynamical properties of plane polynomial automorphisms
This note studies the dynamical behavior of polynomial mappings with polynomial inverse from the real or complex plane to itself.
Convex spectral functions
In this paper we characterize all convex functionals defined on certain convex sets of hermitian matrices and which depend only on the eigenvalues of matrices. We extend these results to certainExpand
Nuclear norm of higher-order tensors
An analogue of Banach's theorem for tensor spectral norm and Comon's conjecture for Tensor rank is established --- for a symmetric tensor, its symmetric nuclear norm always equals its nuclear norm. Expand
Universal uncertainty relations.
A fine-grained uncertainty relation is found that is given in terms of the majorization order between two probability vectors, significantly extending a majorization-based uncertainty relation first introduced in M. H. Partovi, Phys. Expand
Generalized Rank-Constrained Matrix Approximations
An explicit solution to the rank-constrained matrix approximation in Frobenius norm is given, which is a generalization of the classical approximation of an $m\times n$ matrix by a matrix of, at most, rank k. Expand
Regular subgraphs of almost regular graphs
It is shown that if k ≥ 2q − 2 and q is a prime power then G contains a q- regular subgraph (and hence an r-regular subgraph for all r) and that r < q, r ≡ q (mod 2); these results follow from Chevalley's and Olson's theorems on congruences. Expand
The Maximum Number of Perfect Matchings in Graphs with a Given Degree Sequence
It is shown that the number of perfect matchings in a simple graph G with an even number of vertices and degree sequence is at most $ \prod_{i=1}^n (d_i!)^{{1\over 2d-i}}$. Expand
The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems
We consider the formulation and local analysis of various quadratically convergent methods for solving the symmetric matrix inverse eigenvalue problem. One of these methods is new. We study the caseExpand