The eigenvalue decomposition and The Singular Value decomposition of matrices using Jacobi rotation

摘要

Techniques for parsing using the Jacobi rotation matrices. Multiple iterations of Jacobi rotation are conducted on a First array of Complex values of Jacobi matrices with multiple rotation of Complex values to Zero elements that are outside of the diagonal in the Matrix.For each iteration, one can form a subarray based on the first Matrix and can be Decomposed to obtain eigenvectors for the subarray, and can form a rotation matrix with the eigenvectors of Jacobi and can be used to update the first Matrix.A Second Matrix Complex values, which contains vectors orthogonal is derived based on the Jacobi rotation matrices. For The decomposition of the own value can derive a Third Matrix of values based on the rotation of Jacobi matrices.For The Singular Value decomposition of matrix, a fourth and a Left singular Vectors and Singular Value Matrix can be derived based on the Jacobi rotation matrices.