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Recently, in a course of projective geometry, I was introduced to the topic of Quaternions. Since I am just out of Complex Analysis, it seemed natural to wonder how integration would be handled. In the (admittedly little) research I did, I could only find mention of quaternion integration in regard to physics and not really any descriptions. I was hoping someone could point me to a resource on the topic, give an overview, or explain why it's not really a field. Thanks!

J. W. Tanner
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    It depends. How are you defining integration without commutativity? This is not a trivial thing to do, as you can see in the relatively simpler example of matrix integration. – Ninad Munshi Apr 08 '24 at 21:21
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    And quaternions can be modeled as real matrices, https://math.stackexchange.com/questions/287597/matrix-representation-of-the-quaternions , so matrix integration would subsume quaternion integration. – Eric Towers Apr 08 '24 at 21:23
  • @EricTowers not always. A popular sub use case of matrix integration is limiting your attention to vectors and real symmetric matrices (or their symmetrizations), which quaternions are not. But you're right that dealing with that antisymmetric twist part is always the challenge especially with quaternions. – Ninad Munshi Apr 08 '24 at 21:31

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