INVERTIBLE COMPLETIONS OF PARTIAL OPERATOR MATRICES - THE NONSYMMETRIC CASE

We consider nonsymmetric partial operator matrices R whose directed graphs belong to a certain class and for which certain key, fully specified principal submatrices are invertible. Under these circumstances, we prove the existence of a unique invertible completion F of R such that (F-1)ij is block zero whenever R(ij) is unspecified. In this way, the existing results of Johnson and Lundquist are generalized to the nonsymmetric case.