The cyclic rank completion problem with general blocks

Abstract

Listen

Translate article

We present an upper bound for the minimal completion rank of a partial matrix P whose block pattern is a single cycle of size with specified blocks . Under certain conditions, the bound becomes quite sharp when k increases. This extends previous results in which the blocks are regular. The upper bound is constructed from invariants associated with the canonical form of the partial matrix, under row and column operations. These invariants can be expressed in terms of ranks of certain matrices constructed directly from the data blocks, independent of P being in canonical form.