Putzer's Method

While we were discussing the graphical representation of the $2\times 2$ unimodular matrices as ``quaternions'' (that is, ${\bf i}^2=-{\bf 1}$, remaining squares $+{\bf 1}$) and the variants of Euler's formula for $e^{i\phi}$ in quaternion form, an article appeared in Journal of Mathematical Physics [17] purporting to generalize Rodrigues' formula for some particular Lie groups using Putzer's method. This lead to looking up the method, wondering whether the scheme was actually correct, and finally to an understanding of Sylvester's formula for general (meaning non-normal as well as normal) matrices.