The center of the quaternion algebra is the subfield of real quaternions. This lattice is isomorphic to the lattice of Hurwitz quaternions. The real linear span of is isomorphic to the real algebra of quaternions . The multiplication of quaternions is non-commutative. Just as complex numbers can be represented as matrices, so can quaternions. Thus is isomorphic to the unit quaternions. A feature of quaternions is that multiplication of two quaternions is noncommutative. Each of the seven lines generates a subalgebra of O isomorphic to the quaternions H. A similar interpretation is possible for quaternions and Clifford algebras in general. Each 4x4 matrix representation of quaternions corresponds to a multiplication table of unit quaternions. It uses NumPy and can calculate multiple slerp interpolations between the two quaternions. An arithmetic of four dimensions called quaternions was defined by William Rowan Hamilton in 1843. The singularities are also avoided when working with quaternions. This means that there is a homomorphism from quaternions of unit norm to . Dual numbers form the coefficients of dual quaternions.