Add to ORKGHilbert's 17th problem concerns expressing polynomials on Rn as a sum of squares. It is well known that many positive polynomials are not sums of squares; see [R00] [deA preprt] for excellent surveys. In this paper we consider symmetric non-commutative polynomials and call one "matrix positive", if whenever matrices of any size are substituted for the variables in the polynomial the matrix value which the polynomial takes is positive semidefinite. The result in this paper is: A polynomial is matrix positive if and only if it is a sum of squares
The cones of nonnegative polynomials and sums of squares arise as central objects in convex algebrai...
Abstract. We show that all the coefficients of the polynomial tr((A+ tB)m) ∈ R[t] are nonnegative w...
In 1976 Procesi and Schacher developed an Artin–Schreier type theory for central simple algebras wit...
Hilbert's 17th problem concerns expressing polynomials on R n as a sum of squares. It is well k...
We consider the problem of extending the classical S-lemma from commutative case to noncommutative c...
Abstract If a real polynomial f can be written as a sum of squares of real polynomials, then clearly...
A non-commutative polynomial which is positive on a bounded semi-algebraic set of operators has a we...
textabstractThis paper presents a construction for symmetric, non-negative polynomials, which are no...
Abstract. Let M be an archimedean quadratic module of real t × t matrix polynomials in n variables, ...
Abstract. Let M be an archimedean quadratic module of real t × t matrix polynomials in n variables, ...
We give some examples of trace-positive non-commutative quaternary quartics which are not cyclically...
This paper presents a construction for symmetric, non-negative polynomials, which are not sums of sq...
Helton recently proved that a symmetric polynomial in noncommuting variables is positive semidefinit...
Helton recently proved that a symmetric polynomial in noncommuting variables is positive semidefinit...
AbstractWe investigate the representation of multivariate symmetric polynomials as sum of squares, a...
The cones of nonnegative polynomials and sums of squares arise as central objects in convex algebrai...
Abstract. We show that all the coefficients of the polynomial tr((A+ tB)m) ∈ R[t] are nonnegative w...
In 1976 Procesi and Schacher developed an Artin–Schreier type theory for central simple algebras wit...
Hilbert's 17th problem concerns expressing polynomials on R n as a sum of squares. It is well k...
We consider the problem of extending the classical S-lemma from commutative case to noncommutative c...
Abstract If a real polynomial f can be written as a sum of squares of real polynomials, then clearly...
A non-commutative polynomial which is positive on a bounded semi-algebraic set of operators has a we...
textabstractThis paper presents a construction for symmetric, non-negative polynomials, which are no...
Abstract. Let M be an archimedean quadratic module of real t × t matrix polynomials in n variables, ...
Abstract. Let M be an archimedean quadratic module of real t × t matrix polynomials in n variables, ...
We give some examples of trace-positive non-commutative quaternary quartics which are not cyclically...
This paper presents a construction for symmetric, non-negative polynomials, which are not sums of sq...
Helton recently proved that a symmetric polynomial in noncommuting variables is positive semidefinit...
Helton recently proved that a symmetric polynomial in noncommuting variables is positive semidefinit...
AbstractWe investigate the representation of multivariate symmetric polynomials as sum of squares, a...
The cones of nonnegative polynomials and sums of squares arise as central objects in convex algebrai...
Abstract. We show that all the coefficients of the polynomial tr((A+ tB)m) ∈ R[t] are nonnegative w...
In 1976 Procesi and Schacher developed an Artin–Schreier type theory for central simple algebras wit...