The formula of polarization identity is: (x, y) = (1/4) (‖ x+y ‖ 2-‖ x-y ‖ 2) When H is a real space; When h is a complex space, (x, y) = (1/4) (‖ x+y ‖ 2-‖ x-y ‖ 2+i ‖ x+iy ‖ 2-i ‖.

Polarization identity is an important equation that relates the inner product and norm, and it is a formula that expresses the inner product by norm. Let h be the inner product space and ‖ be the norm derived from the inner product (,). There are similar identities for bilinear Hermite functional on real inner product space and bilinear functional φ(x, y) on complex inner product space.

Brief introduction of polarization identity;

Identity, a mathematical concept, is an equation that holds no matter how the variables are taken. The range of identity is the common part of the definition range of left and right functions, but two independent functions have their own definition ranges, which are different from X identity in non-negative real number set and X identity in real number set.

An identity has multiple variables and one variable. If there is only one variable on both sides of the identity, then the identity is the relationship between two analytical expressions. It comes from e ix = cosx+isinx (triangular representation of complex numbers), if x=π, e π I+ 1 = 0.