12/04/2018, 16:00 — 17:00 — Abreu Faro Amphitheatre
João Filipe Queiró, Universidade de Coimbra
Sums and products of equivalence orbits
Similarity and equivalence of matrices over fields are well-understood relations, and that understanding is elementary, specially in the case of equivalence. For matrices over rings – e.g. the integers – the situation is different. Equivalence is still simple and its study leads to the concept of invariant factors of a matrix. About these, several interesting basic questions can be raised. This talk will address two of those questions: how do invariant factors behave under matrix addition and multiplication? Some things are known about these problems, and the second one – already completely solved for certain classes of rings – has deep relations with other parts of mathematics.