## From Rational Canonical Form to The Kostant Section

Suppose we have a $2\times 2$ matrix $$ M = \begin{pmatrix} x_{11} & x_{12}\\ x_{21} & x_{22} \end{pmatrix} $$ with entries in a field $F$. The characteristic polynomial of this matrix is $p(t) := {\rm det}(tI_2 – M) = t^2 – (x_{11} + x_{22})t + x_{11}x_{22} – x_{21}x_{12}$. One might ask: how can we produce […]