E-is-a-euclidian-space-and-f-from-E-to-E-verify-x-y-E-2-x-f-y-f-x-y-prove-that-f-is-linear-

Question Number 50387 by Abdo msup. last updated on 16/Dec/18

$${E}\:{is}\:{a}\:{euclidian}\:{space}\:{and}\:{f}\:\:{from}\:{E}\:{to}\:{E}\:{verify} \\ $$$$\forall\left({x},{y}\right)\:\in{E}^{\mathrm{2}} \:\:\:\:\left({x}\:\mid{f}\left({y}\right)\right)=\left({f}\left({x}\right)\mid{y}\right)\:{prove}\:{that}\:{f}\:{is}\:{linear}. \\ $$

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