Legendre Transformation - Examples

Examples

The exponential function ex has x ln xx as a Legendre transform since their respective first derivatives ex and ln x are inverse to each other. This example shows that the respective domains of a function and its Legendre transform need not agree. As another easy example, for the Legendre transform is

Similarly, the quadratic form

with A a symmetric invertible n-by-n-matrix has

as a Legendre transform.

Read more about this topic:  Legendre Transformation

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