A continuously differentiable function whose derivative (or Jacobian) is invertible at a point is itself invertible on some neighborhood of that point, with a differentiable inverse. It is closely related to, and often proved alongside, the implicit function theorem.
Facts
StatementThe inverse function theorem gives sufficient conditions under which a function has a local inverse near a point, namely that the function's best linear approximation, its derivative, is itself invertible there. 1 Connections
Sources
1. Inverse Function Theorem (Wikipedia)
Wikimedia FoundationLead section and Statements sectionQuote, Lead section and Statements section
In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.