On the Heights of Quaternionic Vectors
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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.
KeywordsQuaternion rank row echelon form rotation
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