grandes-ecoles 2018 Q1

grandes-ecoles · France · centrale-maths1__official Matrices Matrix Norm, Convergence, and Inequality
Let $a$ and $b$ be in $E$. Show the following relation and give a geometric interpretation:
$$\|a + b\|^{2} + \|a - b\|^{2} = 2(\|a\|^{2} + \|b\|^{2})$$
Let $a$ and $b$ be in $E$. Show the following relation and give a geometric interpretation:

$$\|a + b\|^{2} + \|a - b\|^{2} = 2(\|a\|^{2} + \|b\|^{2})$$