Quaternian definition of Quaternian in the Free Online Encyclopedia.

quaternion (kwətûr`nēən), in mathematics, a type of higher complex number first suggested by Sir William R. Hamilton in 1843. A complex number is a number of the form a+bi when a and b are real numbers and i is the so-called imaginary unit defined by the equation i²=−1. The rules for operating with complex numbers are simply those of operating with the polynomial a+bx except that i² is replaced by −1 whenever it occurs. A quaternion, an extension of this concept, is a number of the form a+bi+cj+dk when a, b, c, and d are real numbers and i, j, and k are imaginary units defined by the equations i²=j²=k²=ijk=−1. Quaternions, as well as vectors U [−3,1] and V [5,2], one can add their corresponding components to find the resultant vector R [2,3], or one can graph U and V on a set of coordinate axes and complete the parallelogram formed with U and V
..... Click the link for more information. and tensors tensor, in mathematics, quantity that depends linearly on several vector variables and that varies covariantly with respect to some variables and contravariantly with respect to others when the coordinate axes are rotated (see Cartesian coordinates ).
..... Click the link for more information. (later outgrowths of the concept of quaternions), have many important applications in mechanics.

quaternion [kwə′ter·nē·ən]

(mathematics)

The division algebra over the real numbers generated by elementsi,j,ksubject to the relationsi²=j²=k²= -1 andij= -ji=k,jk= -kj=i, andki= -ik=j. Also known as hypercomplex number.

quaternion (redirected from Quaternian)

quaternion
(redirected from Quaternian)