116 citations · 1.1k across the 72 of their papers we have counts for
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A Model Theoretic Perspective on Matrix Rings
Igor Klep, Marcus Tressl
In this paper natural necessary and sufficient conditions for quantifier elimination of matrix rings in the language of rings expanded by two unary functions, naming the t…
Noncommutative polynomials describing convex sets
J. W. Helton, I. Klep, S. McCullough +1
The free closed semialgebraic set determined by a hermitian noncommutative polynomial is the closure of the connected component of containing…
Bianalytic free maps between spectrahedra and spectraballs
J. William Helton, Igor Klep, Scott McCullough +1
Linear matrix inequalities (LMIs) are ubiquitous in real algebraic geometry, semidefinite programming, control theory and signal processing. LMIs with (dimension free) matrix unkno…
A Matrix Positivstellensatz with lifting polynomials
Igor Klep, Jiawang Nie
Given the projections of two semialgebraic sets defined by polynomial matrix inequalities, it is in general difficult to determine whether one is contained in the other. To address…