An Algorithm for Generating N-Dimensional Rotation Matrix

Abstract

This paper describes a new algorithm for generating an N-dimensional rotation matrix M that rotates a given N-dimensional vector X in the direction of a given N-dimensional vector Y of the same dimension. The N-dimensional Rotation Matrix Generation Algorithm (NRMG) uses two-dimensional rotations to rotate provided vectors X and Y in the direction of coordinate axis x1. Matrix M is created by multiplying matrix MX by the inverse of matrix MY, which rotates the given vectors in the direction of axis x1. RMG algorithm does not determine how the Mx and My matrices are calculated. An algorithm for their calculation using rotations in the coordinate planes is proposed, but they can also be obtained by the Householder transformation, which will be more efficient for "dense" vectors. The prospect of performing parallel calculations of two-dimensional rotations is also investigated.