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How to detect redundant equation from a system of nonlinear equation?

  1. Jul 28, 2010 #1
    How to detect redundant equation from a system of nonlinear equation?
    It means how to find out a system of nonlinear equation is "linear independence"?
    One equation from the system can not be represented by the others in the system of nonlinear equation.
  2. jcsd
  3. Aug 9, 2010 #2
    Welcome gohkgohkgohk .
    I'm afraid there's no general method of spotting a redundant equation from a set. The Jacobian helps a liitle if you have differentiable non-linear equations.
  4. May 8, 2012 #3
    Hi Eynstone, could you share more details on how to determine the redundant equation using Jacobian? My suspection is even its Jacobian matrix has redundant rows, the non-linear equation system may not have redundant equations.
  5. May 26, 2012 #4
    I checked the section on functional dependence from Gerald Folland's Advanced Calculus.

    There it says, if you consider on open set U, then

    Jacobian is zero throughout U if and only if the functions have some (possibly various) functional dependence(s) throughout U.

    So it's not enough for the Jacobian to vanish at a single point, calculus needs an open set to draw conclusions. To deal with single points, I think is part of the practicality of the subject algebraic geometry, which more or less deals with systems of polynomials, as far as I know, but looks like a very abstract subject.
    Last edited: May 26, 2012
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