William Rowan Hamilton

Irish mathematician and astronomer (1805-1865)

{| class="wikitable" align="right" style="text-align:center; margin-left:0.5em; max-width: 230px;" |+ Quaternion multiplication table |- |width=15| !width=15| !width=15| !width=15| !width=15| |- ! | | | | |- ! | | | | |- ! | | | | |- ! | | | | |- |colspan=5| Left column shows the left factor, top row shows the right factor. Also, a\mathbf{b}=\mathbf{b}a and -\mathbf{b} = (-1)\mathbf{b} for a\in \mathbb{R} , \mathbf{b} = \mathbf{i}, \mathbf{j}, \mathbf{k} . |} thumb|Cayley graph of the [[quaternion group showing the six cycles of multiplication by , and . (If the image

quantum operator for the energy

path in a graph that visits each vertex exactly once

theorem that a square matrix satisfies its own characteristic equation

equation in classical mechanics

principle that the dynamics of a physical system are determined by a variational problem of the Lagrangian

symbol used in mathematics, physics and engineering to indicate a differential operator in a Cartesian vector space

In abstract algebra, the biquaternions are the numbers , where , and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group and commute with their coefficients. There are three types of biquaternions corresponding to complex numbers and the variations thereof: Biquaternions when the coefficients are complex numbers. Split-biquaternions when the coefficients are split-complex numbers. Dual quaternions when the coefficients are dual numbers.

In mathematics, a versor is a quaternion whose norm is one, also known as a unit quaternion. Each versor has the form \ u = \exp(a\mathbf{r}) = \cos a + \mathbf{r} \sin a, \qquad \mathbf{r}^2 = -1, \qquad a \in [0,\pi]\ , where the condition \ \mathbf{r}^2 = -1\ means that \ \mathbf{r}\ is an algebraic imaginary unit. There is a sphere of imaginary units in the quaternions. Note that the expression for a versor is just Euler's formula for the imaginary unit \ \mathbf{r} ~. If \ a = \tfrac{\pi}{2}\ (when \ a\ is a right angle), then \ u = \mathbf{r}\ , and it is called a right versor.

vector field associated to a hamiltonian on a symplectic manifold

an optimality condition in optimal control theory

Mathematical game