quaternion, 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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