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Small matrices for irrational nonnegative matrix factorisation

Supervisor

Suitable for

MSc in Computer Science
Computer Science, Part B
Mathematics and Computer Science, Part C
Computer Science and Philosophy, Part C
Computer Science, Part C

Abstract

Recently it was shown (https://arxiv.org/abs/1605.06848) that there is a 6x11-matrix M with rational nonnegative entries so that for any factorisation M = W H (where W is a 6x5-matrix with nonnegative entires, and H is a 5x11-matrix with nonnegative entries) some entries of W and H need to be irrational. The goal of this project is to explore if the number of columns of M can be chosen below 11, perhaps by dropping some columns of M. This will require some geometric reasoning. The project will likely involve the use of tools (such as SMT solvers) that check systems of nonlinear inequalities for solvability.

Prerequisites: The project is mathematical in nature, and a good recollection of linear algebra is needed. Openness towards programming and the use of tools is helpful.