[shiandow]

Don't think I'll ever get used to stars in LaTeX when someone means simple multiplication.

The preceding blog post[1] seems to contain the more interesting parts though. This is just (d/dt)^n e^At x = A^n e^At x, which is kind of obvious from the definition of e^At.

[1]: https://nosferalatu.com/DerivativesLogarithmsTransforms.html

[cycomanic]

The article (even more the previous article) really misses a reference to matrix exponentials [1]. Everything about X(t) = X^t becomes a bit clearer. Also I think using the term transform is a bit loose here. IIRC Matrix exponentials only work with linear transforms that are represented by a square matrix.

[1] https://en.m.wikipedia.org/wiki/Matrix_exponential