There exist large amounts of numerical data that are stored in databases and must be analyzed. Database tables come with a schema and include non-numerical attributes; this is crucial contextual information that is needed for interpreting the numerical values. We propose relational matrix operations that support the analysis of data stored in tables and that preserve contextual information. The result of our approach are precisely defined relational matrix operations and a system implementation in MonetDB that illustrates the seamless integration of relational matrix operations into a relational DBMS.

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.