25 citations · 73 across the 17 of their papers we have counts for
19 papers
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…
Inclusion constants for free spectrahedra with applications to quantum incompatibility
Andreas Bluhm, Eric Evert, Igor Klep +2
Building on the matrix cube problem, inclusions of free spectrahedra have been used successfully to obtain relaxations of hard spectrahedral inclusion problems. The quality of such…
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…
Free extreme points span generalized free spectrahedra given by compact coefficients
Eric Evert
Matrix convexity generalizes convexity to the dimension free setting and has connections to many mathematical and applied pursuits including operator theory, quantum information, n…
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…
Canonical Polyadic Decomposition via the generalized Schur decomposition
Eric Evert, Michiel Vandecappelle, Lieven De Lathauwer
The canonical polyadic decomposition (CPD) is a fundamental tensor decomposition which expresses a tensor as a sum of rank one tensors. In stark contrast to the matrix case, with l…
A recursive eigenspace computation for the Canonical Polyadic decomposition
Eric Evert, Michiel Vandecappelle, Lieven De Lathauwer
The canonical polyadic decomposition (CPD) is a compact decomposition which expresses a tensor as a sum of its rank-1 components. A common step in the computation of a CPD is compu…
Guarantees for existence of a best canonical polyadic approximation of a noisy low-rank tensor
Eric Evert, Lieven De Lathauwer
The canonical polyadic decomposition (CPD) of a low rank tensor plays a major role in data analysis and signal processing by allowing for unique recovery of underlying factors. How…
Convexity of a certain operator trace functional
Eric Evert, Scott McCullough, Tea Štrekelj +1
In this article the operator trace function is introduced and its convexity and concavity properties are investigated.…
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…
Arveson extreme points span free spectrahedra
Eric Evert, J. William Helton
Let denote -tuples of real symmetric matrices. Given tuples and $Y=(Y_1, \dots, Y_g) \in SM_{…
Matrix Convex Sets Without Absolute Extreme Points
Eric Evert
This article shows the existence of a class of closed bounded matrix convex sets which do not have absolute extreme points. The sets we consider are noncommutative sets, , for…
Extreme points of matrix convex sets, free spectrahedra and dilation theory
Eric Evert, J. William Helton, Igor Klep +1
For matrix convex sets a unified geometric interpretation of notions of extreme points and of Arveson boundary points is given. These notions include, in increasing order of streng…
Circular Free Spectrahedra
Eric Evert, J. William Helton, Igor Klep +1
This paper considers matrix convex sets invariant under several types of rotations. It is known that matrix convex sets that are free semialgebraic are solution sets of Linear Matr…
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…