INERTIAS OF BLOCK BAND MATRIX COMPLETIONS

The full set of completion inertias is described in terms of seven lin ear inequalities involving inertias and ranks of specified submatrices . The minimal completion rank for P is computed. We study the completi on inertias of partially specified hermitian block band matrices, usin g a block generalization of the Dym-Gohberg algorithm. At each inducti ve step, we use our classification of the possible inertias for hermit ian completions of bordered matrices. We show that when all the maxima l specified submatrices are invertible, any inertia consistent with Po incare's inequalities is obtainable. These results generalize the nonb lock band results of Dancis [SIAM J. Matrix Anal. Appl., 14 (1993), pg 813-829]. All our results remain valid for real symmetric completions .