In this paper, the quaternion matrix UTV (QUTV) decomposition and quaternion tensor UTV (QTUTV) decomposition are proposed. To begin, the terms QUTV and QTUTV are defined, followed by the algorithms. Subsequently, by employing random sampling from the quaternion normal distribution, randomized QUTV and randomized QTUTV are generated to provide enhanced algorithmic efficiency. Furthermore, theoretical analysis is discussed. Specifically, upper bounds for approximating QUTV and QTUTV are provided, followed by deterministic error bounds and average-case error bounds for the randomized situations. Finally, numerous numerical experiments are presented to verify that the proposed algorithms work more efficiently and with similar relative errors compared to other comparable decomposition methods. This indicates that they could be used in computer vision and other related fields.
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