Identities of matrix algebras (joint work with M. Brešar, I. Klep and C. Procesi.)

We will consider various types of identities of matrix algebras. Trace identities are a generalisation of polynomial identities, and every trace identity is a consequence of the Cayley-Hamilton identity by the second fundamental theorem of matrix invariants. We will show that this is no longer the case for quasi-identities, while it holds for functional identities. We will also present an application of matrix invariants to free analysis.