Inverse function theorem: Difference between revisions

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TheIn Inverse[[mathematics]], Functionthe Theorem'''inverse function theorem''' gives sufficient conditions for a vector valued function to be invertible on an open region containing a point in its ___domain.

The Theorem:

If at pa point P a function ''f'':Rn'''R'''^''n''-->Rn'''R'''^''n'' has a [[Jacobian]] determinant that is nonzero, and ''F'' is continuously differentiable near P, it is an invertible function near pP.

The Jacobian matrix of ''f''^-inverse1 at ''f''(pP) is then the inverse of JfJ''f'', evaluated at f(p)P.