In
mathematics, a
sesquilinear form is a generalization of a
bilinear form that, in turn, is a generalization of the concept of the
dot product of
Euclidean space. A bilinear form is
linear in each of its arguments, but a sesquilinear form allows one of the arguments to be "twisted" in a
semilinear manner, thus the name; which originates from the Latin
numerical prefix meaning "one and a half". The basic concept of the dot product – producing a
scalar from a pair of vectors – can be generalized by allowing a broader range of scalar values and, perhaps simultaneously, by widening the definition of what a vector is.