Companion Operator

A companion matrix is a matrix with a prescribed characteristic polynomial. I would like to show them from a broader perspective: companion matrices are the matrix version of a shift operator.

Read more


Variational Equation

The variational equation is a fundamental tool in engineering. It is the description of the sensitivity with respect to the initial conditions. A remarkable fact, often presented only in \(\mathbf{R}^n\), is that this is in fact the solution of another differential equation, sometimes called the variational equation. I would like to show that this is valid in general manifolds.

Read more