And also assuming that the matrix is not diagonalazible.

For instance.let the matrix be :

$$A=\begin{bmatrix} 2 & 1 \\ 0 & 2 \\ \end{bmatrix}$$

I'm going to take the exponential of it which is $e^A$, not trying to solve a differential equation here so just taking $e^A$ not $e^{At}$.

We all know the formula for the exponential. But the thing is I completely forgot how that formula converges. Anyway since A is not diagonal we can't take the exponential of the entries, what w

  • $\begingroup$ Besides just using the power series, which converges everywhere? $\endgroup$ – Bib-lost Aug 3 '16 at 10:30

Write $A=2I+N$ where $$N=\begin{bmatrix} 0 & 1 \\ 0 & 0 \\ \end{bmatrix}$$

Then $\exp(A)=\exp(2I)\exp(N)$ since $I$ and $N$ commute.

$\exp(N)$ is not too difficult to compute as $N^2=0$...


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.