quaternion (redirected from Quarternions)

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 and tensors (later outgrowths of the concept of quaternions), have many important applications in mechanics.

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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.