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).)

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

Loading...

Similar Threads for need convex concave | Date |
---|---|

A Need (or not) for invoking axiom of choice in a certain case | Sep 13, 2017 |

I Levi-Civita: very small problem, need two steps explained | Sep 23, 2016 |

Intuition and existence for convex neighbourhoods | Mar 10, 2015 |

Stuck with tensors, need a push | Feb 17, 2015 |

Need some help understanding boundary operator on simplicies | Feb 2, 2015 |

**Physics Forums - The Fusion of Science and Community**