Sadly I have failed to understand the euclidean space. For example I have a problem asking me the following: 1. Check that in an euclidean space we have:
$$\left\|x + y\right\|^2 + \left\|x – y\right\|^2 =2( \left\|x\right|^2 +\left\|y|\right\|^2),\ \forall x, y\text{ vectors}$$
Can you please help me understand this kind of problem? Thank you all for your time!