Projection (relational algebra)

In relational algebra, a projection is a unary operation written as ${\displaystyle \Pi _{a_{1},...,a_{n}}(R)}$, where ${\displaystyle R}$ is a relation and ${\displaystyle a_{1},...,a_{n}}$ are attribute names. Its result is defined as the set obtained when the components of the tuples in ${\displaystyle R}$ are restricted to the set ${\displaystyle \{a_{1},...,a_{n}\}}$ – it discards (or excludes) the other attributes.^[1]

In practical terms, if a relation is thought of as a table, then projection can be thought of as picking a subset of its columns. For example, if the attributes are (name, age), then projection of the relation {(Alice, 5), (Bob, 8)} onto attribute list (age) yields {5,8} – we have discarded the names, and only know what ages are present.

Projections may also modify attribute values. For example, if ${\displaystyle R}$ has attributes ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$, where the values of ${\displaystyle b}$ are numbers, then ${\displaystyle \Pi _{a,\ b\times 0.5,\ c}(R)}$ is like ${\displaystyle R}$, but with all ${\displaystyle b}$-values halved.^[2]