25 citations · 73 across the 17 of their papers we have counts for
9 papers · 1 filter
Graded face lifts and free extreme points of free spectrahedra
Eric Evert, Jack Graham
A free spectrahedron is the matricial solution set of a free linear matrix inequality . In this dimension-free setti…
Completely Positive Matrix Products
Eric Evert, Michael T. Jury, Scott McCullough
Building on recent works that investigate positivity preserving matrix products, we {examine} the class of \JCP (\jcp) matrix products. A bilinear map on the Cartesian product of t…
Matrix convex sets over the Euclidean ball and polar duals of real free spectrahedra
Eric Evert, Benjamin Passer
We show that the free spectrahedron determined by universal anticommuting self-adjoint unitaries is not equal to the minimal matrix convex set over the ball in dimension three or h…
Extreme points of matrix convex sets and their spanning properties
Eric Evert, Benjamin Passer, Tea Štrekelj
This expository article gives a survey of matrix convex sets, a natural generalization of convex sets to the noncommutative (dimension-free) setting, with a focus on their extreme…
Matrix Extreme Points and Free extreme points of Free spectrahedra
Aidan Epperly, Eric Evert, J. William Helton +1
A spectrahedron is a convex set defined by a linear matrix inequality, i.e., the set of all such that \[ L_A(x) = I + A_1 x_1 + A_2 x_2 + \dots + A_g x_g \succ…
The Arveson boundary of a Free Quadrilateral is given by a noncommutative variety
Eric Evert
Let denote -tuples of real symmetric matrices and set . A free quadrilateral is the collection of…
Empirical properties of optima in free semidefinite programs
Eric Evert, Yi Fu, J. William Helton +1
Semidefinite programming is based on optimization of linear functionals over convex sets defined by linear matrix inequalities, namely, inequalities of the form $$L_A(X)=I-A_1X_1-\…
Efficient evaluation of noncommutative polynomials using tensor and noncommutative Waring decompositions
Eric Evert, J. William Helton, Shiyuan Huang +1
This paper analyses a Waring type decomposition of a noncommuting (NC) polynomial with respect to the goal of evaluating efficiently on tuples of matrices. Such a decomposi…
Factor posets of frames and dual frames in finite dimensions
Kileen Berry, Martin S. Copenhaver, Eric Evert +4
We consider frames in a finite-dimensional Hilbert space where frames are exactly the spanning sets of the vector space. A factor poset of a frame is defined to be a collection of…