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On page 15 of this note

$\operatorname{End}_{\mathbb C} \mathbb H$ is an $8$-dimensional real vector space.

Is there a simple way to see this?

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  • $\begingroup$ Exactly where does it say that? $\endgroup$ – José Carlos Santos Sep 14 '18 at 15:29
  • $\begingroup$ @JoséCarlosSantos Line -12 of page 15. $\endgroup$ – rschwieb Sep 14 '18 at 15:30
  • $\begingroup$ @rschwieb Thank you. $\endgroup$ – José Carlos Santos Sep 14 '18 at 15:32
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$\mathbb H$ is a $2$-dimensional $\mathbb C$ vector space, so $\operatorname{End}_\mathbb C(\mathbb H)\cong M_2(\mathbb C)$. The latter is, of course, is $8$ dimensional considered as an $\mathbb R$ vector space.

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