- quaternion identity
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quaternion identity
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Quaternion — Quaternions, in mathematics, are a non commutative extension of complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three dimensional space. They find uses in both… … Wikipedia
Quaternion group — In group theory, the quaternion group is a non abelian group of order 8. It is often denoted by Q and written in multiplicative form, with the following 8 elements : Q = {1, −1, i , − i , j , − j , k , − k }Here 1 is the identity element, (−1)2 … Wikipedia
Dual quaternion — The set of dual quaternions is an algebra that can be used to represent spatial rigid body displacements.[1] A dual quaternion is an ordered pair of quaternions  = (A, B) and therefore is constructed from eight real parameters. Because rigid… … Wikipedia
Split-quaternion — Coquaternion multiplication × 1 i j k 1 1 i j k i i −1 k −j j j −k +1 −i … Wikipedia
Lagrange's identity — In algebra, Lagrange s identity is the identity:iggl( sum {k=1}^n a k^2iggr) iggl(sum {k=1}^n b k^2iggr) iggl(sum {k=1}^n a k b kiggr)^2 = sum {i=1}^{n 1} sum {j=i+1}^n (a i b j a j b i)^2 iggl(= {1 over 2} sum {i=1}^n sum {j=1}^n (a i b j … Wikipedia
Euler's four-square identity — In mathematics, Euler s four square identity says that the product of two numbers, each of which being a sum of four squares, is itself a sum of four squares. Specifically::(a 1^2+a 2^2+a 3^2+a 4^2)(b 1^2+b 2^2+b 3^2+b 4^2)=,::(a 1 b 1 a 2 b 2 a… … Wikipedia
Quaternions and spatial rotation — Unit quaternions provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock. Compared to… … Wikipedia
Rotation matrix — In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix rotates points in the xy Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian… … Wikipedia
Cross product — This article is about the cross product of two vectors in three dimensional Euclidean space. For other uses, see Cross product (disambiguation). In mathematics, the cross product, vector product, or Gibbs vector product is a binary operation on… … Wikipedia
Charts on SO(3) — In mathematics, the special orthogonal group in three dimensions, otherwise known as the rotation group SO(3), is a naturally occurring example of a manifold. The various charts on SO(3) set up rival coordinate systems: in this case there cannot… … Wikipedia
Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… … Wikipedia
