Names and origin upright=1.25|thumb|right|According to Sarrus's rule, the determinant of a 3×3 matrix involves multiplications between matrix elements identified by crossed diagonals In 1842, William Rowan Hamilton first described the algebra of quaternions and the non-commutative Hamilton product. In particular, when the Hamilton product of two vectors (that is, pure quaternions with zero scalar part) is performed, it results in a quaternion with a scalar and vector part. The scalar and vector part of this Hamilton product corresponds to the negative of dot product and cross product of the two vectors.
Names and origin upright=1.25|thumb|right|According to Sarrus's rule, the determinant of a 3×3 matrix involves multiplications between matrix elements identified by crossed diagonals In 1842, William Rowan Hamilton first described the algebra of quaternions and the non-commutative Hamilton product. In particular, when the Hamilton product of two vectors (that is, pure quaternions with zero scalar part) is performed, it results in a quaternion with a scalar and vector part The scalar and vector part of this Hamilton product corresponds to the negative of dot product and cross product of the two vectors.