On the Heights of Quaternionic Vectors

In this paper, we introduce a new numerical character, namely the height, for a quaternionic vector. According to this new concept (height), we give a complete classification of quaternionic vectors and enumerate all possible row echelon forms of the associated matrices for each type of the quaternionic vectors. By observing a link which the height has with the system of Cartesian frames, we give the character descriptions for several types of the systems of Cartesian frames.