We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding is that the key factor forcing a zero entry in this inverse matrix is a certain "conditional triangularity property" of the orthogonal polynomials associated with the measure.
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View Measures with zeros in the inverse of their moment matrix