sesquillinear form

sesquillinear form

[¦ses·kwə‚lin·ē·ər ′fȯrm] (mathematics) A mapping ƒ(x, y) from E × F into R, where R is a commutative ring with an automorphism with period 2 and E × F is the cartesian product of two modules E and F over R, such that for each x in E the function which takes y into ƒ(x, y) is antilinear, and for each y in F the function which takes x into ƒ(x, y) is linear.