File Name: rotations quaternions and double groups .zip
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Published: 22.04.2021
Learn more. Johannes C. Familton Columbia U. Citations per year. Abstract: arXiv. References
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This paper is an attempt to simplify and clarify the mathematical language used to express quaternionic quantum mechanics QQM. Barred operators represent the key to realizing a set of translation rules between quaternionic and complex quantum mechanics QM. These translations enable us to obtain a rapid quaternionic counterpart of standard quantum mechanical results. This is a preview of subscription content, access via your institution. Rent this article via DeepDyve.
Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Altmann Published Mathematics Mathematics Magazine. The invention of the calculus of quaternions is a step towards the knowledge of quantities related to space which can only be compared, for its importance, with the invention of triple coordinates by Descartes.
Learn more. Merab Gogberashvili Tbilisi, Inst. Published in: Eur.
The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for quaternions occurred to him while he was walking along the Royal Canal on his way to a meeting of the Irish Academy, and Hamilton was so pleased with his discovery that he scratched the fundamental formula of quaternion algebra,. The set of quaternions is denoted , , or , and the quaternions are a single example of a more general class of hypercomplex numbers discovered by Hamilton. While the quaternions are not commutative, they are associative, and they form a group known as the quaternion group. By analogy with the complex numbers being representable as a sum of real and imaginary parts , , a quaternion can also be written as a linear combination. Note also that NonCommutativeMultiply i. A variety of fractals can be explored in the space of quaternions.
We discuss 3-D rotations by which one double-couple earthquake source can be rotated into another arbitrary double-couple.
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