  We study the expressive power of the LARA language -- a recently proposed
unified model for expressing relational and linear algebra operations -- both
in terms of traditional database query languages and some analytic tasks often
performed in machine learning pipelines. We start by showing LARA to be
expressive complete with respect to first-order logic with aggregation. Since
LARA is parameterized by a set of user-defined functions which allow to
transform values in tables, the exact expressive power of the language depends
on how these functions are defined. We distinguish two main cases depending on
the level of genericity queries are enforced to satisfy. Under strong
genericity assumptions the language cannot express matrix convolution, a very
important operation in current machine learning operations. This language is
also local, and thus cannot express operations such as matrix inverse that
exhibit a recursive behavior. For expressing convolution, one can relax the
genericity requirement by adding an underlying linear order on the domain.
This, however, destroys locality and turns the expressive power of the language
much more difficult to understand. In particular, although under complexity
assumptions the resulting language can still not express matrix inverse, a
proof of this fact without such assumptions seems challenging to obtain.
