Category:Inverse Function Theorem

This category contains pages concerning Inverse Function Theorem:

Let $n \in \N$ be a natural number.

Let $f: \R^n \to \R^n$ be a mapping on the real Cartesian space of $n$ dimensions.

Let $\mathbf x \in \R^n$ be an element of $\R^n$.

Let the Jacobian matrix of $f$ be non-singular in the locality of $\mathbf x$.

Then there exists a local single-valued differentiable inverse for $f$ at the locality of $\mathbf x$.