1. 实数情形：
$$\langle x,y\rangle=\frac14(\langle x+y,x+y\rangle-\langle x-y,x-y\rangle).$$
2. 复数情形：
$$\langle x,y\rangle=\frac14(\langle x+y,x+y\rangle-\langle x-y,x-y\rangle+i\langle x+iy,x+iy\rangle-i\langle x-iy,x-iy\rangle).$$
3. 算子情形：
$$\langle x,Ty\rangle=\frac14(\langle x+y,T(x+y)\rangle-\langle x-y,T(x-y)\rangle+i\langle x+iy,T(x+iy)\rangle-i\langle x-iy,T(x-iy)\rangle).$$
原文：http://www.cnblogs.com/wzhhwy/p/3980337.html