Hello, I'm reading this book http://freescience.info/go.php?pagename=books&id=1041 about differential manifolds. In the appendix this book gives a proof for the inverse function theorem. It assumes that the Jacobian matrix [tex]Df_a[/tex] is invertible (where [itex]a[/itex] is a location where it is calculated), and then it says: "By an affine transformation [itex]x\mapsto Ax+b[/itex] we can assume that [itex]a=0[/itex] and [itex]Df_a=1[/itex]." Isn't this the same thing, as assuming that all invertible matrices are diagonalizable? And isn't that assumption wrong?