Polarization identity solves the problem of vector quantity product at the starting point of * * *, which can transform the operation of quantity product into the most intuitive problem of line segment length, avoiding the reference of angle and the generation of multivariable in the process of solving problems. In the real problems of college entrance examination every year, we can find problems that can be solved by polarization identity, especially some problems related to the maximum value of product, which can avoid setting points and establish a system.

The problem of converting the maximum value into the maximum value related to the line segment. Polarization identity has parallelogram mode and triangle mode, and there is no difference between them. In a quadrilateral, the vector product of the same starting point is related to the length of the diagonal of the parallelogram with this as its adjacent side, while in a triangle, the vector product of the same starting point is related to the length of the opposite side and the length of the middle line of the opposite side.

In all the maximum problems, we often encounter the situation that both the opposite side and the middle line are known but unknown, so that we can find the line segment length that meets the maximum requirements. 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.

Identity is a mathematical concept, and it is an equation that holds no matter how the variables are taken. The scope of identity is the common part of the meaning domain of the fixed beat resistance kernel of left and right functions, but two independent functions have their own definition domains, which are the same as X in the non-negative real number set and different in the real number set.

Derivation of plane vector polarization identity;

When h is a real space, (x, y) = (1/4) (‖ x+y ‖ 2-‖ x-y ‖ 2); When h is a complex space, (x, y) = (1/4) (‖ x+y ‖ 2-‖ x-y ‖ 2+i ‖ x+iy ‖ 2-i ‖. The bilinear Hermite function in the real inner product space and the bilinear φ(x, y) function in the complex inner product space have similar identities.

If y=f(x) and y=g(x) have the same domain and f(x)=g(x) exists for any x in the domain, then y=f(x) and y=g(x) are equivalent functions, and the two analytical expressions must be the same. If y=f(x) and y=g(x) are equal functions, then the analytical expressions of these two functions are the same, so the parameters in them can be equal accordingly.