In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the theory side, we prove that our algorithm is more efficient that other existing methods. Moreover, our algorithm is optimal in the sense of the least number of complex inversions. On the practice side, our algorithm outperforms existing algorithms on randomly generated matrices. We argue that this algorithm can be used to improve the practical utility of recursive Strassen-type algorithms by providing the fastest possible base case for the recursive decomposition process when applied to quaternion matrices.

翻译：本文推导并分析了一种用于求逆四元数矩阵的算法。该算法是复数矩阵求逆的Frobenius算法的类比。在理论方面，我们证明了该算法比其他现有方法更高效。此外，就复数求逆的最少次数而言，该算法具有最优性。在实践方面，我们的算法在随机生成的矩阵上优于现有算法。我们论证了，该算法能为递归Strassen型算法（当应用于四元数矩阵时）提供尽可能最快的基例，从而改进其实际效用。