The quaternions involved abandoning the commutative law, a radical step for the time. In the context of this prototype geometric algebra, Hamilton also introduced the cross and dot products of vector algebra, the quaternion product being the cross product minus the dot product as scalar. Hamilton also described a quaternion as an ordered four-element multiple of real numbers, and described the first element as the "scalar" part, and the remaining three as the "vector" part. He coined the neologisms "tensor" and "scalar", and was the first to use the word "vector" in the modern sense.
The quaternions involved abandoning the commutative law a radical step for the time In the context of this prototype geometric algebra Hamilton also introduced the cross and dot products of vector algebra the quaternion product being the cross product minus the dot product as scalar Hamilton also described a quaternion as an ordered four-element multiple of real numbers and described the first element as the "scalar" part and the remaining three as the "vector" part He coined the neologisms "tensor" and "scalar" and was the first to use the word "vector" in the modern sense