for each , if all of the variables but are held constant, then is a linear function of . One way to visualize this is to imagine two orthogonal vectors; if one of these vectors is scaled by a factor of 2 while the other remains unchanged, the cross product likewise scales by a factor of two. If both are scaled by a factor of 2, the cross product scales by a factor of .

A multilinear map of one variable is a linear map,