Inverse function theorem: Difference between revisions

Revision as of 20:03, 18 February 2004

Revision as of 20:05, 18 February 2004

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:''f'':'''R'''^''n''-->'''R'''^''n''

has a [[Jacobian]] determinant that is nonzero, and ''F'' is continuously differentiable near ''P'', it is an invertible function near ''P''. That is, an [[inverse function]] exists, in some [[neighborhood]] of ''F(P)''.

The Jacobian matrix of ''f''^-1 at ''f''(''P'') is then the inverse of J''f'', evaluated at P.