bilinear form (redirected from Skew form)

bilinear form [¦bī‚lin·ē·ər ′fȯrm]

(mathematics)

A polynomial of the second degree which is homogeneous of the first degree in each of two sets of variables; thus, it is a sum of terms of the forma_ijx_iy_j, wherex₁, … ,x_mandy₁, … ,y_nare two sets of variables and thea_ijare constants.

More generally, a mapping ƒ(x, y) fromE×FintoR, whereRis a commutative ring andE×Fis the Cartesian product of two modulesEandFoverR, such that for eachxinEthe function which takesyinto ƒ(x, y) is linear, and for eachyinFthe function which takesxinto ƒ(x, y) is linear.