Can I read Legendre Transformation in Geometry on EtoBox?
Legendre Transformation in Geometry by joaoluisprado is a document available to read on EtoBox.
What is Legendre Transformation in Geometry about?
The document discusses the Legendre transformation, which relates a convex function F(x) to its convex conjugate F*(y) through a change of variables. It explains how the graph of F(x) can be viewed dually as the intersection of supporting half-spaces parameterized by y = ∇F(x). This yields F*(y) = maxx {xTy - F(x)}. Legendre transforms provide a dual representation of the same shape and underlie information geometry through Bregman divergences. Properties like self-duality and strict convexity of conjugates
- Author
- joaoluisprado
- Language
- EN