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portada Split-biquaternion
Type
Physical Book
Publisher
Language
English
Format
Paperback
ISBN13
9786131227301

Split-biquaternion

New Book Imported to Netherlands
Delivery: 23 Oct - 27 Oct Shipping: 13 to 14 business days.
€ 162,73
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Synopsis "Split-biquaternion"

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a split-biquaternion is a member of the Clifford algebra C 0,3(R). This is the geometric algebra generated by three orthogonal imaginary unit basis directions, {e1, e2, e3} under the combination rule e_i e_j = Bigg{ begin{matrix} -1 & i=j, - e_j e_i & i not = j end{matrix} giving an algebra spanned by the 8 basis elements {1, e1, e2, e3, e1e2, e2e3, e3e1, e1e2e3}, with (e1e2)2 = (e2e3)2 = (e3e1)2 = 1 and ( = e1e2e3)2 = +1. The sub-algebra spanned by the 4 elements {1, i = e1, j = e2, k = e1e2} is the division ring of Hamilton''s quaternions, H = C 0,2(R) One can therefore see that Cl_{0,3}(mathbb{R}) = mathbb{H} otimes mathbb{D} where D = C 1,0(R) is the algebra spanned by {1, }, the algebra of the split-complex numbers. Equivalently, Cl_{0,3}(mathbb{R}) = mathbb{H} oplus mathbb{H}. Because of this isomorphism, the term "split biquaternion" is archaic and no longer used much by mathematicians.

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