A short definition of an RDBMS may be a DBMS in which data is stored in the form of tables and the relationship among the data is also stored in the form of tables.
The first systems that were relatively faithful implementations of the relational model were from the University of Michigan; Micro DBMS (1969) and from IBM UK Scientific Centre at Peterlee; IS1 (1970–72) and its followon PRTV (1973–79). The first system sold as an RDBMS was Multics Relational Data Store, first sold in 1978. Others have been Berkeley Ingres QUEL and IBM BS12.
The most popular definition of an RDBMS is a product that presents a view of data as a collection of rows and columns, even if it is not based strictly upon relational theory. By this definition, RDBMS products typically implement some but not all of Codd's 12 rules.
A second, theory-based school of thought argues that if a database does not implement all of Codd's rules (or the current understanding on the relational model, as expressed by Christopher J Date, Hugh Darwen and others), it is not relational. This view, shared by many theorists and other strict adherents to Codd's principles, would disqualify most DBMSs as not relational. For clarification, they often refer to some RDBMSs as Truly-Relational Database Management Systems (TRDBMS), naming others Pseudo-Relational Database Management Systems (PRDBMS).
Low adoption costs associated with open-source RDBMS products such as MySQL, PostgreSQL and public domain RDBMS libraries such as SQLite have begun influencing vendor pricing and licensing strategies .