Exponential of Jordan Form

Asked Jan 09 '21 at 07:05

Active Jan 09 '21 at 09:39

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Let J be a single 4 x 4 Jordan block with lambda on the diagonal. Write the matrix e^Jt.

Would you help me about this? What should I do with e^Jt? I can find the exp(J) but are there any difference with 'Jt'?

my e^J form is {e^l,e,1,1},{1,e^l,e,1},{1,1,e^l,e},{1,1,1,e^l} l=lambda

edited Jan 09 '21 at 09:39

asked Jan 09 '21 at 07:05

Mamito

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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Jan 09 '21 at 07:20
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Hint: first work out the formula for the $n$th power of a Jordan block. Then expand the exponential as a power series. – user7530 Jan 09 '21 at 07:43
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If I understand your question correctly, just replace $J$ in $\exp(J)$ by $Jt$! That is $\exp(Jt)=I+Jt+\frac{1}{2}(Jt)^2+\frac{1}{6}(Jt)^3+\ldots$ – Fakemistake Jan 09 '21 at 10:51
There is a closed formula for the exponential of a Jordan block. See here for an example with a $3\times 3$ Jordan block. – Fakemistake Jan 10 '21 at 10:17

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