A relational DBMS provides limited functionality to build multivariate statistic models, which require extensive vector and matrix manipulation. This talk discusses how to extend a DBMS with basic vector and matrix operators by programming User-Defined Functions (UDFs). UDFs represent a C API that allows the definition of scalar and aggregate functions that can be used in SQL. We explain UDF features and limitations to implement vector and matrix operations commonly used in statistics and machine learning, paying attention to DBMS, operating system and computer architecture constraints. UDFs have several advantages and limitations. On one hand, a UDF allows fast evaluation of arithmetic expressions, memory manipulation, using multidimensional arrays and exploiting all C language control statements. But on the other hand, a UDF cannot execute disk I/O instructions, the amount of heap and stack memory that can be allocated is small and the UDF C code must take into account somewhat specific architecture characteristics of the DBMS. We discuss experiments comparing UDFs and SQL with respect to performance, ease of use, flexibility and scalability. UDFs are shown to be a good alternative to implement primitive vector and matrix operations because they are faster than standard SQL aggregations and as efficient as plain SQL arithmetic expressions.