Assume a norm \( \| \cdot \| \) is defined by an inner product . Then
\[ \|x + y\|^2 + \|x - y\|^2 = 2\|x\|^2 + 2\|y\|^2, \quad \forall x, y \in X. \]Assume a norm \( \| \cdot \| \) is defined by an inner product . Then
\[ \|x + y\|^2 + \|x - y\|^2 = 2\|x\|^2 + 2\|y\|^2, \quad \forall x, y \in X. \]