  In this paper we pursue the study of spectral categories initiated in [26].
More precisely, we construct the Universal matrix invariant of spectral
categories, i.e. a functor U with values in an additive category Add, which
inverts the Morita equivalences, satisfies matrix invariance, and is universal
with respect to these two properties. For example, the algebraic K-theory and
the topological Hochschild and cyclic homologies are matrix invariants, and so
they factor uniquely throw U. As an application, we obtain for free non-trivial
trace maps from the Grothendieck group to the topological Hochschild homology
ones.
