I have been trying to figure this out for a couple weeks now. Why does the Legendre transform require that the function be convex?(adsbygoogle = window.adsbygoogle || []).push({});

Is it because g(x) has to be solved to get x(g) and finding this inverse means g(x) should be bijective? (And if g is bijective then dg/dx will always be positive or always be negative [or perhaps one spot be zero] which means always convex (or always concave).)

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# Why do you need a convex/concave function to do a Legendre transform?

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