##  [Legendre Transform](/legendre-transform) 

  ##  [Legendre Transform](https://natural.quantumdictionary.io/legendre-transform-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An operation that maps a (convex, proper, lower semicontinuous) function f(x) of a variable x to its convex conjugate f*(p) = sup_x (p·x − f(x)), exchanging variable and slope and producing a dual representation.