Quick Fact Check if $A$ and $B$ Commute, $\exp((A+B)t)= \exp(At)\cdot\exp(Bt)$?

Question

If $A$ and $B$ Commute, $\exp((A+B)t)= \exp(At)\cdot\exp(Bt)$? is this statement true?

Answer 1

It is in fact the case. For a thorough explanation, please see my answer to this question. It's only a mouse click away!

Hope this helps. Cheerio,

and as always,

Fiat Lux!!!

Answer 2

if $A\cdot B=B\cdot A$

then $e^{A+B}=e^{A}\cdot e^{B}$

now multiply both side by $t$

we have

$e^{At+Bt}$,

you can apply same rule for this too

there is question related to matrix expoenntial

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