کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775745 | 1631745 | 2017 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Multivector and multivector matrix inverses in real Clifford algebras
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We show how to compute the inverse of multivectors in finite dimensional real Clifford algebras Cl(p, q). For algebras over vector spaces of fewer than six dimensions, we provide explicit formulae for discriminating between divisors of zero and invertible multivectors, and for the computation of the inverse of a general invertible multivector. For algebras over vector spaces of dimension six or higher, we use isomorphisms between algebras, and between multivectors and matrix representations with multivector elements in Clifford algebras of lower dimension. Towards this end we provide explicit details of how to compute several forms of isomorphism that are essential to invert multivectors in arbitrarily chosen algebras. We also discuss briefly the computation of the inverses of matrices of multivectors by adapting an existing textbook algorithm for matrices to the multivector setting, using the previous results to compute the required inverses of individual multivectors.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 311, 15 October 2017, Pages 375-389
Journal: Applied Mathematics and Computation - Volume 311, 15 October 2017, Pages 375-389
نویسندگان
Eckhard Hitzer, Stephen Sangwine,