Hermitian and normal completions
Hugo J. Woerdeman · Linear and Multilinear Algebra · 1997
The problems of finding the minimal and maximal possibie negative and positive inertia for partial Hermitian banded matrices has been solved without any nonsingularity restrictions on the given blocks. The solution has striking similarities with minimal rank completion results. Applications to Hermitian matrix (in)equalities are presented. In addition, the minimal normal completion problem is introduced.