Projection (Relational Algebra)

relational-algebra

Definition

Projection (Relational Algebra)

The projection operation ${\pi }_{A_1,\dots ,A_k}:\text{Relation}\to \text{Relation}$ selects a subset of attribute $\{A_1,\dots ,A_k\}$ from a relation $R$ and maps it to a new relation $R^{\prime }$ containing only those attributes, i.e.

$$R^{\prime }={\pi }_{A_1,A_2,\dots ,A_k}(R)=\{T[A_1,A_2,\dots ,A_k]\mid T\in R\}$$

Where $T[A_1,A_2,\dots ,A_k]$ is a new tuple containing only the values from the attribute specified in the list $\{A_1,\dots ,A_k\}$ for a given tuple $T$. Since the resulting relation $R^{\prime }$ is a set, any duplicate tuple that arise from this operation are automatically eliminated.

Note that there’s also the possibility for extended projection, meaning specifying expressions instead of attributes, i.e.:

$${\pi }_{name,salary÷12}(instructors)$$