cyclic equivalence

Rational sums of hermitian squares of free noncommutative polynomials

  • Kristijan Cafuta
  • Igor Klep
  • Janez Povh
    • Categories Global Optimization, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , , , , , , , , ,

    In this paper we consider polynomials in noncommuting variables that admit sum of hermitian squares and commutators decompositions. We recall algorithms for finding decompositions of this type that are based on semidefinite programming. The main part of the article investigates how to find such decomposition with rational coefficients if the original polynomial has rational coefficients. … Read more

    On the nonexistence of sum of squares certificates for the BMV conjecture

  • Kristijan Cafuta
  • Igor Klep
  • Janez Povh
    • Categories Basic Sciences Applications, Semi-definite Programming Tags , , , , ,

    The algebraic reformulation of the BMV conjecture is equivalent to a family of dimensionfree tracial inequalities involving positive semidefinite matrices. Sufficient conditions for these to hold in the form of algebraic identities involving polynomials in noncommuting variables have been given by Markus Schweighofer and the second author. Later the existence of these certificates has been … Read more