Euler and De Moivre’s Formulas for Fundamental Matrices of Commutative Quaternions
نویسندگان
چکیده
منابع مشابه
De- Moivre’s and Euler Formulas for Matrices of Split Quaternions
In this paper, real matrix representations of split quaternions are examined in terms of the casual character of quaternion. Then, we give De-Moivre’ s formula for real matrices of timelike and spacelike split quaternions, separately. Finally, we state the Euler theorem for real matrices of pure split quaternions.
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An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.
متن کاملinvolution matrices of real quaternions
an involution or anti-involution is a self-inverse linear mapping. in this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. moreover, properties and geometrical meanings of these matrices will be given as reflections in r^3.
متن کاملInvolution Matrices of Real Quaternions
An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R.
متن کاملExplicit Formulas for Bernoulli and Euler Numbers
Explicit and recursive formulas for Bernoulli and Euler numbers are derived from the Faá di Bruno formula for the higher derivatives of a composite function. Along the way we prove a result about composite generating functions which can be systematically used to derive such identities.
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ژورنال
عنوان ژورنال: International Electronic Journal of Geometry
سال: 2020
ISSN: 1307-5624
DOI: 10.36890/iejg.768821