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...

and quaternions, the last of which made him one of the founders of modern linear algebra. He has made major contributions in optics, classical mechanics...

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

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

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

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

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

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

subspace. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford...

{\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...

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

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

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

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

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...

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

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

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

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

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

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...

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

associative division algebras are the real numbers, complex numbers and quaternions.: 366  As STA is not a division algebra, some STA elements may lack an...

{\displaystyle S^{3}} ; as a group, it may be identified with the group of unit quaternions. The Heisenberg group is a connected nilpotent Lie group of dimension...

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...

{H}}} are used for the Hamiltonian operator in quantum mechanics and ℋ for the Hamiltonian function in classical Hamiltonian mechanics. In mathematics...

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...

orientation of a rigid body, including a set of three Euler angles, a quaternion, or a direction cosine matrix (also referred to as a rotation matrix)...