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188宝金博页面版: QuaternionsandGroups - Brown University

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内容提示: Quaternions and GroupsRich SchwartzOctober 16, 20141 What is a Quaternion ?A quaternion is a symbol of the forma + bi + cj + dk,where a,b,c,d are real numbers and i,j,k are special symbols that obey thefollowing algebraic rules.i 2 = j 2 = k 2 = ?1,ij = k, jk = i, ki = j,ji = ?k, kj = ?i, ik = ?j,ix = xi, jx = xj, kx = xk, for all real xQuaternions are added componentwise, like vectors. For instance(3 + 4i + j) + (7 + 2j + k) = 10 + 4i + 3j + k.Quaternions are multiplied according to the foil method. J...

文档格式:PDF | 页数:10 | 浏览次数:26 | 上传日期:2016-03-24 04:44:43 | 文档星级:
Quaternions and GroupsRich SchwartzOctober 16, 20141 What is a Quaternion ?A quaternion is a symbol of the forma + bi + cj + dk,where a,b,c,d are real numbers and i,j,k are special symbols that obey thefollowing algebraic rules.i 2 = j 2 = k 2 = −1,ij = k, jk = i, ki = j,ji = −k, kj = −i, ik = −j,ix = xi, jx = xj, kx = xk, for all real xQuaternions are added componentwise, like vectors. For instance(3 + 4i + j) + (7 + 2j + k) = 10 + 4i + 3j + k.Quaternions are multiplied according to the foil method. Just expand every-thing out, and then use the rules above to simplify the expression so that itlooks like a quaternion. For instance(4 + j)(i + k) = 4i + 4k + ji + jk = 4i + 4k − k + i = 5i + 3k.Quaternions are often denoted by single variables, like complex numbers. Forinstanceq = a + bi + cj + dj.1

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