inverse function theorem


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inverse function theorem

[′in‚vərs ′fənk·shən ‚thir·əm]
(mathematics)
If ƒ is a continuously differentiable function of euclidean n-space to itself and at a point x0 the matrix with the entry (∂ƒi /∂ xj )x0in the i th row and j th column is nonsingular, then there is a continuously differentiable function g (y) defined in a neighborhood of ƒ(x0) which is an inverse function for ƒ(x) at all points near x0.
References in periodicals archive ?
By the Inverse Function Theorem [6, p.373], it follows that the mapping [PSI(*) is locally injective.
We then have [N.sub.0](y)) = y for x [greater than or equal to] 2 and y [greater than or equal to] 0, and by the inverse function theorem, [N.sub.0](y) is monotonic increasing in y for y [greater than or equal to] 0.
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