# Non-singular derivative definition

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?

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