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Suppose we have $q_1\sim \mathcal N(\mu_1,\Sigma_1)$ and $q_2\sim\mathcal N(\mu_2,\Sigma 2)$ two independent Gaussian Random Variables that represent two quaternions. Consider: $$ q_3 = q_1\otimes q_2 $$

Is $q_3$ also a Gaussian Random Variable?

space_voyager
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    There's no reason to use the tensor symbol $\otimes$ for quaternion multiplication. – arctic tern May 10 '17 at 06:58
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    Note it's not even true for reals: https://math.stackexchange.com/q/101062/11323 – Kimball May 10 '17 at 22:40
  • @arctictern a frustrating and confusing practice that started in the aerospace engineering literature. I appologize for the crimes of my people :-( – JMJ Jun 05 '17 at 19:26

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