# Minimal Rank Completions for Overlapping Blocks

arXiv: https://arxiv.org/abs/2106.11267 · HTML: https://mlsanity.com/paper/2106.11267/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2021.

## Built on by (most cited first, 1 of 1)

- [Tensor Train Completion from Fiberwise Observations Along a Single Mode](https://mlsanity.com/paper/2509.18149/) (2025)

## Abstract (arXiv)

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.