In this paper, we address the problem of restoring orthogonality a numerically noisy 4D rotation matrix by finding its nearest (in Frobenius norm) correct matrix. This can be straightforwardly solved using Singular Value Decomposition (SVD). Nevertheless, to avoid numerical methods, present two new closed-form methods. One relies on direct minimization mentioned norm, and other passage double q...

In this paper we present two algorithms for the computation of a diagonal form of a matrix over non-commutative Euclidean domain over a field with the help of Gröbner bases. This can be viewed as the preprocessing for the computation of Jacobson normal form and also used for the computation of Smith normal form in the commutative case. We propose a general framework for handling, among other, o...