ATTENTION/WARNING - NE PAS DÉPOSER ICI/DO NOT SUBMIT HERE

Ceci est la version de TEST de DIAL.mem. Veuillez ne pas soumettre votre mémoire sur ce site mais bien à l'URL suivante: 'https://thesis.dial.uclouvain.be'.
This is the TEST version of DIAL.mem. Please use the following URL to submit your master thesis: 'https://thesis.dial.uclouvain.be'.
 

Matrix completion and graph rigidity: exploiting surprising similarities

Thibeau, Marie
(2022)

Files

Thibeau_20441700_2022.pdf
  • Open access
  • Adobe PDF
  • 796.82 KB
Download

Details

Supervisors
Hendrickx, Julien
Faculty
Ecole polytechnique de Louvain
Degree label
Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée
Abstract
This master thesis addresses the problem of uniqueness of matrix completion by means of the graph rigidity results. The state of the art studies the existing results in both rigidity theory and matrix completion problem. It allows to determine that no author who addressed the question of the uniqueness of matrix completion using the results of graph rigidity, tried to directly reproduce the combinatorial results of Laman in two dimensions. A summary of Laman's results allows their good understanding in order to reproduce them in the context of matrix completion. A necessary and sufficient condition is found for the uniqueness of matrix completion. Finally, a pebble game algorithm allows to show whether a given matrix is uniquely completable.