For each n × n positive semidefinite matrix A we define the minimal index I (A)=max{λ ⪰ 0 : A ο B ⪰ λB for all B ⪰ 0} and, for each norm N, the N-index I_N(A) = min{N(A ο B): B ⪰0 and N(B) = 1}, where A ο B = [aij bij] is ...

We study the Lovász–Schrijver lift-and-project operator (LS +) based on the cone of symmetric, positive semidefinite matrices, applied to the fractional stable set polytope of graphs. The problem of obtaining a combinatorial ...

Let A be an n×n complex Hermitian matrix and let λ(A)=(λ1,…,λn)∈Rn denote the eigenvalues of A, counting multiplicities and arranged in non-increasing order. Motivated by problems arising in the theory of low rank matrix ...