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## Definición

Dados 3 espacios vectoriales V, W y X sobre el mismo cuerpo F, un operador bilineal es una función

${\displaystyle B\colon V\times W\to X}$

tal que para todo w en W (fija), la asignación

${\displaystyle v\mapsto B(v,w)}$

es un operador lineal de V a X, y para todo v en V (fija), la asignación

${\displaystyle w\mapsto B(v,w)}$

es un operador lineal de W a X.

• ${\displaystyle B(x,y)=0}$ si x=0 o y=0, siendo 0 el vector nulo.