Search results
Results From The WOW.Com Content Network
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 set A is a ring (in fact a domain) and a lattice and is called the ring of Hurwitz quaternions. There are 24 unit quaternions in this ring, and they are the vertices of a regular 24 cell with Schläfli symbol {3,4,3}.
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 ]
For example, the Hurwitz quaternions form a maximal order in the quaternions with rational co-ordinates; they are not the quaternions with integer coordinates in the most obvious sense. Maximal orders exist in general, but need not be unique: there is in general no largest order, but a number of maximal orders.
In mathematics, quaternions are a non-commutative number system that extends the complex numbers.Quaternions and their applications to rotations were first described in print by Olinde Rodrigues in all but name in 1840, [1] but independently discovered by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space.
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.
Excess weight is a contributing factor in as many as 1,300 additional deaths per day in the U.S., or nearly 500,000 per year, according to the report.
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 ]