Questions tagged [quaternions]
The quaternions tag has no usage guidance.
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Dirac’s debt to Hamilton
According to Tobias Hurter’s popular exposition Too Big for a Single Mind (narrated in the present tense):
Dirac makes use of an elegant mathematical tool developed by the Irish mathematician William ...
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Hamilton's pocket-book entry on quaternions
I've long known the story of Hamilton carving the defining equations of the quaternions into the Broome (aka Brougham) Bridge, and have been aware for some years that there is no trace of the original ...
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What set of criteria led Hamilton to discover the quaternions?
Frobenius's theorem states that the only finite-dimensional, associative division algebras over $\mathbb R$ are: $\mathbb R, \mathbb C, \mathbb H$ (where the last of these are the quaternions). So one ...
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Whatever happened to quaternions?
Quaternions were made up by Hamilton. They are an extension of complex numbers. It is said that he first introduced "3d tertions". He was thinking what the relation between $\bf i$ and $\bf ...
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How did Hamilton conclude the quaternions had to be four dimensional?
I have seen many times before that Hamilton started off believing he would need a three-dimensional system over the reals in order to describe 3D rotations. He considered numbers of the form $a + bi + ...
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Why are quaternions more popular than tessarines despite being non-commutative?
Is this simply because of marketing, hype, etc?
The bicomplex numbers (especially tessarines) look just great being commutative and all.
Images source:https://citeseerx.ist.psu.edu/viewdoc/download?...
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Did Maxwell originally write his equations using quaternions?
I read somewhere, some time ago that Maxwell originally wrote his eponymous equations using the formalism of quaternions and it was only the later intervention of Gibbs and Heaviside that put them ...
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Gauss's anticipation of quaternions and their relation to congruences
Recently i read the article "Hamilton, Rodrigues, Gauss, Quaternions and Rotations: A Historical Reassessment", which can be found freely on the internet. This article is by far the most comprehensive ...
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