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

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...

expressions are referred to as classical Hamiltonian quaternions. Hamilton's innovation consisted of expressing quaternions as an algebra over R. The formulae...

(obsolete), the norm used on the quaternion algebra in William Rowan Hamilton's work; see Classical Hamiltonian quaternions § Tensor Symmetric tensor, a tensor...

\mathbb {R} } , the complex numbers C {\displaystyle \mathbb {C} } and the quaternions H {\displaystyle \mathbb {H} } together with special automorphism groups...

It is based on the concept of a Hamiltonian path in graph theory. Hamilton, Sir W.R. (1853), Lectures on Quaternions Dublin: Hodges and Smith Hamilton...

supplanted the earlier system of quaternions invented by William Rowan Hamilton. Euler's laws of motion History of classical mechanics List of eponymous laws...

matrix Hamiltonian numbers (or quaternions) In physics: Hamiltonian constraint Hamiltonian fluid mechanics Hamiltonian operator, see Hamiltonian (quantum...

(1993). "Quaternion mechanics and electromagnetism". Annales de la Fondation Louis de Broglie. 18 (2): 213–219. Lambek, Joachim. "QUATERNIONS AND THREE...

phase space. Hamiltonian mechanics Metaplectic group Orthogonal group Paramodular group Projective unitary group Representations of classical Lie groups...

{\displaystyle {\frac {1}{kT}}} , known as thermodynamic beta, H is the Hamiltonian of the classical system in terms of the set of coordinates q i {\displaystyle...

classical potential energy term, as well as momentum terms like the classical kinetic energy term. A key difference is that relativistic Hamiltonians...

Theorie der vielfachen Kontinuität, and Hamilton's discovery of the quaternions and John T. Graves' discovery of the octonions in 1843 marked the beginning...

gradient of a scalar potential field Hamiltonian vector field, a vector field defined for any energy function or Hamiltonian Killing vector field, a vector...

configuration space; this is the convention in both the Hamiltonian formulation of classical mechanics, and in Lagrangian mechanics. The symbol p {\displaystyle...

{\boldsymbol {H}}} Hamiltonian in quantum mechanics Hankel function Heaviside step function Higgs boson Hydrogen Set of quaternions Hat matrix H0 is either...

generated by iσ1, iσ2, iσ3 functions identically (is isomorphic) to that of quaternions ( H {\displaystyle \mathbb {H} } ). All three of the Pauli matrices can...

the algebra is isomorphic to the quaternions H. Cl2,0(R) ≅ Cl1,1(R) is isomorphic to the algebra of split-quaternions. Cl0,3(R) is an 8-dimensional algebra...

to represent orientations, rotation quaternions are typically called orientation quaternions or attitude quaternions. To consider rigid body dynamics in...

(2018). "The Mechanization of Ciphers". Classical Cryptology. Ell, Todd A.; Sangwine, Stephen J. (2007). "Quaternion involutions and anti-involutions". Computers...

1123G. doi:10.1119/1.10202. Hamilton, W. R. (1847). "Applications of Quaternions to Some Dynamical Questions". Proceedings of the Royal Irish Academy...

formulas in terms of complex quaternions It is easy to put these Lorentz transformation formulas in terms of complex quaternions or biquaternions by making...

of uniformity Special relativity Deriglazov, Alexei (2010). Classical Mechanics: Hamiltonian and Lagrangian Formalism. Springer. p. 111. ISBN 978-3-642-14037-2...

Jordan–Hölder theorem. Dedekind and Miller independently characterized Hamiltonian groups and introduced the notion of the commutator of two elements. Burnside...

(also called momentum–energy or momenergy) is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is...

fields, and fluid flow. Vector calculus was developed from the theory of quaternions by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century...

composed of quaternions, H = (Hij)n i,j=1. Its distribution is invariant under conjugation by the symplectic group, and it models Hamiltonians with time-reversal...

the Hamiltonian operator in quantum mechanics and H {\displaystyle {\mathcal {H}}} (or ℋ ) for the Hamiltonian function in classical Hamiltonian mechanics...

additional hypotheses, to be either the real numbers, complex numbers, or the quaternions, as is needed for Gleason's theorem to hold.: §3  By invoking Gleason's...

Weiss, Paul (7 July 1941). "On some applications of quaternions to restricted relativity and classical radiation theory". Proceedings of the Royal Irish...