inverse function theorem
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inverse function theorem[′in‚vərs ′fənk·shən ‚thir·əm]
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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.