Multiple points of view
It's often useful and interesting to study an object or result from
many different points of view.
Sometimes yields easy proofs,
sometimes sheds light on the result,
or on the POV.
[connections are one of the richest parts of math]
For instance, in linear algebra,
one can study operators on a vector space
\begin{itemize}
\item module-theoretically
\item Lie-theoretically
\item linear-algebraically (what structures on a vector space does it preserve)
\item via matrices
\end{itemize}
For instance, Schur decomposition
- ?
- preserves a flag
- upper-triangulizability