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Utility of Quaternions in Physics
Alexander McAulay
James Zimmerhoff
其他書名
Quaternions Are a Number System That Extends the Complex Numbers
出版
CreateSpace Independent Publishing Platform
, 2017-06-18
主題
Mathematics / Algebra / Abstract
Political Science / General
Science / Physics / Mathematical & Computational
ISBN
1548174823
9781548174828
URL
http://books.google.com.hk/books?id=Cx-5tAEACAAJ&hl=&source=gbs_api
註釋
In math, the quaternions are a number method that extends the complex numbers. They were originally described by the mathematician William Rowan Hamilton and applied to mechanics in space (3D). Quaternions characteristics are that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two lines in 3D (the quotient of two vectors). Quaternions find uses in theoretical and applied mathematics, in particular for calculations involving 3D rotations such as in computer graphics, computer vision, and crystallographic texture analysis. In useful applications, they find use alongside other methods, like Euler angles and rotation matrices, depending on the application. In contemporary mathematical language, quaternions form a 4D associative normed division algebra over the real numbers, and consequently also a domain. In fact, the quaternions were the elementary noncommutative division algebra to be discovered. According to the Frobenius theorem, it is one of only two finite-dimensional dividing rings containing the real numbers as a proper subring, and the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of whichever quaternions are the largest associative algebra.