$3\times 3$ Matrix exponent

Asked May 22 '23 at 22:48

Active May 22 '23 at 23:11

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I have a problem where I’m given the matrix $$ B = \begin{pmatrix} 1 & 1 & 0\\ 0 & 1 & 1\\ 0 & 0 & 1 \end{pmatrix}. $$

I’m tasked with computing $e^B$. Now the point where I’m struggling is how exactly to commence, seeing as $B$ can’t be diagonalized and its Jordan Normal Form is itself. Plugging it into the power series will give me an infinite sum seeing as B isn’t nilpotent. So how do I compute $e^B$?

edited May 22 '23 at 22:56

Cameron L. Williams

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asked May 22 '23 at 22:48

Sebastian Gersmeier

1

There is a pretty nice pattern for the entries of $B^n$. Did you try computing the first several powers? – Cameron L. Williams May 22 '23 at 22:53
Hint: Write $B=I+N$ where $I$ is the identity matrix and $N$ is nilpotent. – coiso May 22 '23 at 23:13

$3\times 3$ Matrix exponent

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