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?
2026-04-03 06:16:35.1775196995
Is the product of two Guassian quaternions a Gaussian quaternion?
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