Inverse Function Theorem

Given a smooth function f:R^n->R^n, if the Jacobian is invertible at 0, then there is a neighborhood U containing 0 such that f:U->f(U) is a diffeomorphism. That is, there is a smooth inverse f^(-1):f(U)->U.

See also

Diffeomorphism, Implicit Function Theorem, Jacobian

This entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd. "Inverse Function Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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