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In this paper, we further the study of spectral categories initiated in [ 31 ]. Our main contribution is the construction of the  Universal matrix invariant  of spectral categories, that is, a functorwith values in an additive category, which inverts the Morita equivalences, satisfies matrix invariance, and is universal with respect to these two properties. For example, algebraic  K -theory and topological Hochschild and cyclic homologies are matrix invariants and so they factor (uniquely) through. As an application, we obtain a bijective correspondence between the elements of the stable groups of spheres and the trace maps from the Grothendieck group to the topological Hochschild homology groups.

Matrix Invariants of Spectral Categories