Maximal rank Hermitian completions of partially specified hermitian matrices Original Research Article

In this note it is shown that, for a given partially specified hermitian matrix P, the maximal rank for arbitrary (possibly nonhermitian, complex) completions can be attained by hermitian completions. A simple formula for the maximal rank for nonhermitian completions was computed previously by Cohen et al. We also discuss the same situation for symmetric matrices over an arbitrary field, and show that the field size may be critical in establishing the same formulas. Finally, we discuss the same questions under Toeplitz structure, and show that for the matrix image the maximal completion rank is 3 for complex hermitian Toeplitz completions, 3 for real symmetric completions, 3 for real Toeplitz completions, but only 2 for real symmetric Toeplitz completions.