Definition of The Frechet Derivative: Informally: A Frechet derivative is a derivative (slope) defined for mappings from one vector space to another.

The first e in Frechet should have an accent aigu.

Formally (this taken more or less directly from Tripathi, 1996):

Let T be a transformation defined on an open domain U in a normed space X and mapping to a range in a normed space Y.

( Holding fixed an x in U and for each h in X, if a linear and continuous operator L (mapping from X to Y) exists such that:

lim_{||h|| falls to 0} (1/||h||) * (||T(x+h)-T(x)-L(h)||) = 0

Then the operator L, often denoted T'(x), is the Frechet derivative of T() and we can say T is Frechet differentiable at x. (Econterms)

Terms related to The Frechet Derivative:

• Frechet differentiable