CARTESIAN PRODUCT (Relational Operation)

The binary operation CARTESIAN PRODUCT (or CROSS PRODUCT), denoted by $\times$ , creates a relation that combines tuples from two operands in a combinatorial fashion.

The result of $R (A_{1}, A_{2}, \dots, A_{n}) \times S (B_{1}, B_{2}, \dots, B_{m})$ is a relation with degree $n$ + $m$ attributes: $Q (A_{1}, A_{2}, \dots, A_{n}, S (B_{1}, B_{2}, \dots, B_{m})$ . The resulting relation state has one tuple for each combination of tuples - one from $R$ and one from $S$ .

Operands do not have to be type-compatible.

Generally, cross product is not meaningful but it can precede other operations. To keep only combinations where the DEPARTMENT is related to the EMPLOYEE, we can add a SELECT operation:

F E M A L E_{E M P S} E M P N A M E S E M P_{D E P E N D E N T S} A C T U A L_D E P S R E S U L T \leftarrow σ_{S E X =^{'} F^{'}} (E M P L O Y E E) \leftarrow π_{FNAME, LNAME, SSN} (F E M A L E_{E M P S}) \leftarrow E M P N A M E S \times D E P E N D E N T \leftarrow σ_{S S N = E S S N} (E M P_{D E P E N D E N T S}) \leftarrow π_{F N A M E, L N A M E, D E P E N D E N T_{N} A M E} (A C T U A L_D E P S)

Archive Notes

Explorer

CARTESIAN PRODUCT (Relational Operation)

Graph View

Backlinks