Post by mondo on Nov 12, 2022 18:17:52 GMT
On the top of page 157 author shows a matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ and says it corresponds to a Mobius transformation $M(z) = -\frac{1}{z}$. But why?
We have some complex number $z = a + ib$, if we multiply it by above matrix we get \begin{pmatrix} -b \\ a \end{pmatrix} hence $M(z) = -b + ia$. So we transformed $z = a + ib$ into $M(z) = -b + ia$ and to me it corresponds to a transformation $iz = i(a + ib) = ia - b$.
We have some complex number $z = a + ib$, if we multiply it by above matrix we get \begin{pmatrix} -b \\ a \end{pmatrix} hence $M(z) = -b + ia$. So we transformed $z = a + ib$ into $M(z) = -b + ia$ and to me it corresponds to a transformation $iz = i(a + ib) = ia - b$.
