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… Expand

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 certain… Expand

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

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

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

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

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

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 case… Expand