The real rank of monomials

  • Mario Denis Kummer (MPI MiS, Leipzig)
Hörsaal Otto-von-Guericke Universität Magdeburg (Magdeburg)


We consider the problem of determining the real rank of a real homogeneous polynomial f of degree d, i.e. the smallest possible number r such that f can be written as a sum of r dth powers of real linear forms. In geometric complexity theory the real rank of a polynomial is considered — among other notions of rank — as a measure of the computational complexity of evaluating the polynomial. After some general preliminaries we will present upper and lower bounds on the real rank of a monomial and we characterize those monomials for which the lower bound is attained. This is joint work with Enrico Carlini, Alessandro Oneto and Emanuele Ventura.

Mirke Olschewski

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