# Quaternion definitions

A set of four persons or items.

noun

A set of four.

noun

Any number of the form

*a*+*bi*+*cj*+*dk*where*a, b, c,*and*d*are real numbers,*ij*=*k, i*^{2}=*j*^{2}= −1, and*ij*= −*ji.*Under addition and multiplication, quaternions have all the properties of a field, except multiplication is not commutative.noun

An expression that is the sum of four terms, one of which is real and three of which contain imaginary units, and that can be written as the sum of a scalar and a three-dimensional vector.

noun

Any number of the form

*a*+*bi*+*cj*+*dk*where*a, b, c,*and*d*are real numbers,*ij*=*k, i*^{2}=*j*^{2}= −1, and*ij*= −*ji.*Under addition and multiplication, quaternions have all the properties of a field, except that multiplication is not commutative.### Origin of quaternion

Middle English

*quaternioun**from*Late Latin*quaterniō**quaterniōn-**from*Latin*quaternī**by fours**from**quater**four times*kwetwer- in Indo-European roots