非退化矩阵的酉相似性
Unitary Similarity of Nonderogatory Matrices
AI总结：
针对非退化矩阵的酉相似性验证问题，提出一种基于几何方法的稳定且高效的数值解法。
摘要：
本文致力于矩阵酉相似性的验证问题。对于非退化矩阵的情况，我们基于几何方法提出了该问题的新解法。该方法的主要优势在于对初始上三角矩阵中的误差具有稳定性。由于上三角形式通常通过近似方法（例如QR算法）获得，上述优势显得更为重要，并使我们能够提出一种数值稳定且高效的矩阵酉相似性验证方法。
英文摘要：
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main advantage of this approach is stability with respect to errors in the initial upper triangular matrix. Since an upper triangular form is usually obtained by approximate methods (e.g. by QR algorithm), the mentioned advantage seems even more significant and allows us to propose the numerically stable and efficient method for verification of matrices for unitary similarity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
