Binary operator

Examples

If a broad definition of "binary operation" is used, such that the inputs and output do not have to be from the same set, then scalar multiplication (${\displaystyle a{\vec {v}}}$) is an binary operator from a scalar and a vector to a vector, and dot product (${\displaystyle {\vec {u}}\cdot {\vec {v}}}$) is a binary operator from two vectors to a scalar.