In mathematics, the 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 states that if at a point P a function
- f:Rn → Rn
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 Jf, evaluated at P.