Operator Matrices with Chordal Inverse Patterns
Charles R. Johnson, Michael E. Lundquist · Birkhäuser Basel eBooks · 1992
We consider invertible operator matrices whose conformally partitioned inverses have 0 blocks in positions corresponding to a chordal graph. In this event, we describe a) block entry formulae that express certain blocks (in particular, those corresponding to 0 blocks in the inverse) in terms of others, under a regularity condition, and b) in the Hermitian case, a formula for the inertia in terms of inertias of certain key blocks.