Projection (relational algebra)

In <a href="/facts/Relational_algebra/7tjTFXdf">relational algebra</a>, a projection is a <a href="/facts/Unary_operation/kb6CkgsX">unary operation</a> written as 
 
 
 
 
 Π
 
 
 a
 
 1
 
 
 ,
 .
 .
 .
 ,
 
 a
 
 n
 
 
 
 
 (
 R
 )
 
 
 {\displaystyle \Pi _{a_{1},...,a_{n}}(R)}
 
, where 
 
 
 
 R
 
 
 {\displaystyle R}
 
 is a <a href="/facts/Relation_(database)/Sj67AUyD">relation</a> and 
 
 
 
 
 a
 
 1
 
 
 ,
 .
 .
 .
 ,
 
 a
 
 n
 
 
 
 
 {\displaystyle a_{1},...,a_{n}}
 
 are attribute names. Its result is defined as the <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> obtained when the components of the <a href="/facts/Tuples/BI1HIxL8">tuples</a> in 
 
 
 
 R
 
 
 {\displaystyle R}
 
 are restricted to the set 
 
 
 
 {
 
 a
 
 1
 
 
 ,
 .
 .
 .
 ,
 
 a
 
 n
 
 
 }
 
 
 {\displaystyle \{a_{1},...,a_{n}\}}
 
 – it discards (or excludes) the other attributes.
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 
 
 
 
 R
 
 
 {\displaystyle R}
 
 has attributes 
 
 
 
 a
 
 
 {\displaystyle a}
 
, 
 
 
 
 b
 
 
 {\displaystyle b}
 
, 
 
 
 
 c
 
 
 {\displaystyle c}
 
, where the values of 
 
 
 
 b
 
 
 {\displaystyle b}
 
 are numbers, then

Π
          
            a
            ,
             
            b
            ×
            0.5
            ,
             
            c
          
        
        (
        R
        )
      
    
    {\displaystyle \Pi _{a,\ b\times 0.5,\ c}(R)}

is like 
 
 
 
 R
 
 
 {\displaystyle R}
 
, but with all 
 
 
 
 b
 
 
 {\displaystyle b}
 
-values halved.

Projection (relational algebra) open-in-new

Projection (relational algebra)