I am working on the palindromic
eigenvalue problem. Palindromes are woerds that read the same from the
front and the back, like mom, dad, rotor.
Transferring the principle to eigenvalue problems yields $Ax=lambda
A^Tx$. $A$ is a quadratic matrix, $A^T$ its transpose, $x$ is a vector
and $lambda$ a number. The fact that $A$ and its transpose are
involved implies many effects. E.g., one can show that if $lambda$ is
an eigenvalue than so is $1 / lambda$.
The palindromic eigenvalue problem arises in a number of engeneering problems, e.g., the modelling of high speed trains or the time discrete optimal control problem.
This work is part of the project C4  of the
research center MATHEON , sponsored by the German Research Council.