Minimal Rank Completions for Overlapping Blocks
arXiv:2106.11267 · doi:10.1016/j.laa.2021.06.011
Abstract
We consider the multi-objective optimization problem of choosing the bottom left block-entry of a block lower triangular matrix to minimize the ranks of all block sub-matrices. We provide a proof that there exists a simultaneous rank-minimizer by constructing the complete set of all minimizers.
11 pages, 1 figure, accepted in Linear Algebra and its Applications