Jacobi method for quaternion matrix singular value decomposition

Abstract

The study of quaternion matrices has gained interest in many areas in recent years, and the problem of diagonalizing such matrices has also attracted attention. In this article, we present an algorithm for computing the SVD of a matrix with quaternion coefficients directly in quaternion arithmetic using a generalization of classical complex Jacobi methods. The extension of the Jacobi transformation to the quaternion case is introduced for the diagonalization of a Hermitian quaternion valued matrix. Based on this, an implicit Jacobi algorithm is proposed for computing the SVD of a quaternion matrix. The performance of the proposed algorithm is presented and compared with an already known algorithm using a complex equivalent of the quaternion matrix, and shown to be superior in execution time and accuracy.