The positive definite completion problem relative to a subspace Original Research Article

We consider the problem of completing a partial real symmetric matrix so that its quadratic from is positive (semi-)definite on a subspace, presented as the null space of a given matrix. Under the appropriate definition of “partial positive definite” the classical result regarding chordal patterns is extended to this setting. However, unlike the classical setting, there are differences between the positive semi-definite and positive definite completion problems.