Abstract
Every proper orthogonal matrix A can be writtenwhere Q is a skew matrix [6], and conversely every such matrix A is orthogonal. It is also known that every proper orthogonal transformation in real Euclidean four-space may be characterized in term of quaternions [1, 3] by the equationdetermines with the origin a vector having the coordinates (XQ, XI, x2, x3). The relationship between these two representations was clearly shown by Murnaghan [5].
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