  Analytical queries often require a mixture of relational and linear algebra
operations applied to the same data. This poses a challenge to analytic systems
that must bridge the gap between relations and matrices. Previous work has
mainly strived to fix the problem at the implementation level. This paper
proposes a principled solution at the logical level. We introduce the
relational matrix algebra (RMA), which seamlessly integrates linear algebra
operations into the relational model and eliminates the dichotomy between
matrices and relations. RMA is closed: All our relational matrix operations are
performed on relations and result in relations; no additional data structure is
required. Our implementation in MonetDB shows the feasibility of our approach,
and empirical evaluations suggest that in-database analytics performs well for
mixed workloads.
