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I'm a bit new to real analysis. Today, I came across this particular equality, whcih seems obvious to me. $$ \lVert x + z \rVert^2 + \lVert x - z \rVert^2 = 2 \lVert x \rVert^2 + 2\lVert z \rVert^2 $$ Is there a specific name for this?

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This is the parallelogram law of norms induced by inner products.

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  • $\begingroup$ Thank you so much! $\endgroup$ – JaP Mar 19 at 19:32

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