MAXIMAL RANK HERMITIAN COMPLETIONS OF PARTIALLY SPECIFIED HERMITIAN MATRICES

In this note it is shown that, for a given partially specified hermiti an matrix P, the maximal rank for arbitrary (possibly nonhermitian, co mplex) 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 sym metric 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 ma trix [GRAPHICS] the maximal completion rank is 3 for complex hermitian Toeplitz completions, 3 for real symmetric completions, 3 for real To eplitz completions, but only 2 for real symmetric Toeplitz completions .