Inverse function theorem: Difference between revisions

Revision as of 16:45, 15 October 2004

Revision as of 16:46, 15 October 2004

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The theorem states that if at a point ''P'' a function ''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.

[[Category:Multivariate calculus]]