Unitary Similarity of Nonderogatory Matrices
For numerical linear algebra practitioners, this provides a stable method to check unitary similarity, addressing instability issues in existing approaches.
This paper presents a new geometric method for verifying unitary similarity of nonderogatory matrices that is stable with respect to errors in the initial upper triangular form, enabling a numerically stable and efficient verification process.
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.