In mathematics, quaternions are a non-commutative number system that extends the complex numbers. Quaternions and their applications to rotations were...

The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by H . {\displaystyle \mathbb {H} .} Quaternions are not a field...

pre-existing concepts: the Imperial Quaternions and the Imperial Eagle (double-headed eagle). The so-called imperial quaternions (German: Quaternionen der Reichsverfassung...

Heaviside Utility of Quaternions in Physics (1893) Alexander McAulay Vector Analysis and Quaternions (1906) Alexander Macfarlane Twenty of the ancillary articles...

originally right versors in Hamilton's quaternions.) The mathematics of ∇ received its full exposition at the hands of P. G. Tait. After receiving Smith's...

be used to multiply any two hyperbolic quaternions. Unlike the ordinary quaternions, the hyperbolic quaternions are not associative. For example, ( i j...

Hamilton's quaternions as pencils of planes. In both cases the real numbers form the axis of a pencil. In Hamilton quaternions there is a sphere of imaginary...

The Quaternion Society was a scientific society, self-described as an "International Association for Promoting the Study of Quaternions and Allied Systems...

In mathematics, the dual quaternions are an 8-dimensional real algebra isomorphic to the tensor product of the quaternions and the dual numbers. Thus...

Hamilton invented quaternions, a mathematical entity in 1843. This article describes Hamilton's original treatment of quaternions, using his notation...

Real non-zero quaternions always have a real positive norm. Real quaternions can represent spatial rotations but only the complex quaternions have the richness...

of Lagrangian mechanics. His career included the analysis of geometrical optics, Fourier analysis, and quaternions, the last of which made him one of...

while the group S p ( 1 ) = S 3 {\displaystyle Sp(1)=S^{3}} of unit-length quaternions instead acts on quaternionic n {\displaystyle n} -space H n =...

problems History of topos theory Hyperbolic quaternion Indian mathematics Islamic mathematics Italian school of algebraic geometry Kraków School of Mathematics...

Kimura, Shunkichi (3 October 1895). "To Friends and Fellow Workers in Quaternions" (PDF). Nature. 52 (1353): 545–546. Bibcode:1895Natur..52..545M. doi:10...

form ordered pairs (p, q) of quaternions p and q, with multiplication and conjugation defined exactly as for the quaternions: ( p , q ) ( r , s ) = ( p...

quantities and quaternions" in 68 pages with contents listed on page 69. Tevfik's book refers on page 11 to Introduction to Quaternions by Kelland and...

(1909/10). The Wikiversity: History of Lorentz transformations via quaternions and hyperbolic numbers includes contributions of James Cockle (1848), Homersham...

{CD}}(\mathbb {H} ,1)} . Much as quaternions can be defined as pairs of complex numbers, the octonions can be defined as pairs of quaternions. Addition is defined...

additional structure of a distinguished subspace. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex...

One rendition of the coat of the empire was the "Quaternion Eagle" (so named after the imperial quaternions) printed by David de Negker of Augsburg, after...

with the quaternions, split-quaternions are not commutative, but further contain nilpotents; they are isomorphic to the square matrices of dimension...

Hamilton's quaternions with Hermann Grassmann's algebra and revealing the geometric nature of these systems, especially in four dimensions. The operations of geometric...

The history of mathematical notation covers the introduction, development, and cultural diffusion of mathematical symbols and the conflicts between notational...

direct sum of the division ring of quaternions with itself is denoted H ⊕ H {\displaystyle \mathbf {H} \oplus \mathbf {H} } . The product of two elements...

y2 and split-complex numbers with quadratic form x2 − y2, quaternions and split-quaternions, octonions and split-octonions. Every composition algebra...

"lines" of elliptic geometry are geodesic curves and, unlike the lines of Euclidean geometry, are of finite length. The algebra of quaternions provides...

of the next hypercomplex number system of double dimensions obtained via the Cayley–Dickson construction. For example, the 4-dimensional quaternions H...

Bibliography of Quaternions (1904) published by the Quaternion Society. He was also one of the personalities, who contributed to the foundation of the Warsaw...

described in terms of quaternions. In general, if a vector [a1, a2, a3] is represented as the quaternion a1i + a2j + a3k, the cross product of two vectors can...