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I have been struggling with this question. What is the significance of finding the rank of a Jacobian matrix of a function?

I understand that the Rank of a matrix signifies the number of linearly independent rows / columns. How does this idea extend to finding the rank of a Jacobian matrix?

Thanks !! :)

Jugesh
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    See http://math.stackexchange.com/questions/48306/jacobian-matrix-rank-and-dimension-of-the-image You may want to read the discussion after Theorem 9.32 in Rudin (page 231). – wj32 Oct 31 '12 at 03:52

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If the Matrix has not a zero determinant it is called the full rank Jacobian. It means if J is Jacobian matrix. det(J) must not be zero to have the full rank.

Bhavik Patel
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