Completions of partial Jordan and Hessenberg matrices (Q1344066)

A matrix completion problem is a problem of finding all completions of a given partial matrix with specific properties. This paper studies specifically the completion of partial Jordan matrices. An algorithm is given for constructing completions of a given partial Jordan matrix having prescribed eigenvalues and multiplicities. The most interesting aspect of the paper is the graph-theoretic interpretation given to the completion algorithm. As an extension, the completions of the partial Hessenberg matrices are also discussed.