The truncated tracial moment problem asks to characterize when a finite sequence of real numbers can be represented with tracial moments of matrices,
i.e., the measure is the trace of the evaluations of monomials on the set of
symmetric matrices. To tackle the problem we can use the tools from linear
algebra. We associate to the sequence the truncated moment matrix and
study its properties, which ether prove or disprove existence of the measure.
In the diploma thesis we statistically analyze the conjecture, that in the
quartic bivariate case with a positive definite 7 × 7 moment matrix, there
exists a measure consisting of one atom of size 2 and at most six atoms of
size 1. The main technique is to subtract the multiple of a moment matrix
of rank 1, such that we get a moment matrix of rank 6, for which we can use
known results about the existence of a measure, that translate the problem
to the feasibility of certain semidefinite programs.
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