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Every Hurwitz quaternion can be factored as a product of irreducible quaternions. This factorization is not in general unique, even up to units and order, because a positive odd prime p can be written in 24( p +1) ways as a product of two irreducible Hurwitz quaternions of norm p , and for large p these cannot all be equivalent under left and ...
The Hurwitz quaternion order is a specific order in a quaternion algebra over a suitable number field. The order is of particular importance in Riemann surface theory, in connection with surfaces with maximal symmetry , namely the Hurwitz surfaces . [ 1 ]
Thus, the quaternion components ,,, are either all integers or all half-integers, depending on whether is even or odd, respectively. The set of Hurwitz quaternions forms a ring; that is to say, the sum or product of any two Hurwitz quaternions is likewise a Hurwitz quaternion.
Adolf Hurwitz (German: [ˈaːdɔlf ˈhʊʁvɪts]; 26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, analysis, geometry and number theory. Early life [ edit ]
Hurwitz and Frobenius proved theorems that put limits on hypercomplexity: Hurwitz's theorem says finite-dimensional real composition algebras are the reals , the complexes , the quaternions , and the octonions , and the Frobenius theorem says the only real associative division algebras are , , and .
The quaternions are a non-commutative extension of the complex numbers which have numerous applications in mathematics, physics, and computer graphics The main article for this category is Quaternion .
Three men were convicted on Monday of murder, conspiracy and other charges for drugging and robbing patrons at gay bars in New York City in 2022, resulting in the deaths of two men.
In mathematics, a versor is a quaternion of norm one (a unit quaternion).Each versor has the form = = + , =, [,], where the r 2 = −1 condition means that r is a unit-length vector quaternion (or that the first component of r is zero, and the last three components of r are a unit vector in 3 dimensions).