The cyclic rank completion problem with regular blocks
Nir Cohen, Edgar Pereira · Linear and Multilinear Algebra · 2017
A tight upper bound is obtained for the minimal completion rank of a partial block matrix P whose block pattern is a single bipartite cycle of order 2k and with specified blocks of order n having non-vanishing determinant. The problem is studied in terms of two auxiliary matrix problems of independent interest, in which a difference between two matrices is divided into ‘small-rank steps’.