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I have a basic definition question. I am studying inverse function theorem, and I am stuck with what it means to say that for a $f'$ is non-singular? I looked it up in the internet, but it did not help. And the book does not give a definition of what non-singularity means. Could someone please help me with it?

Thanks in advance!

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In the multivariable setting, f' is a linear transformation, i.e. a matrix. They mean that this matrix is invertible, i.e. has nonzero determinant.

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  • $\begingroup$ And if the matrix $f'$ is not a square matrix, are we talking about the left inverse or the right inverse? $\endgroup$ – mercury0114 Dec 3 '17 at 15:16

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