Quaternions and the eigenproblem: A new Jacobi algorithm and its convergence

This thesis shows how the Jacobi method for computing eigenvalues and eigenvectors of real symmetric matrices can be enhanced by using Hamilton's quaternions.;First we show that the rich isomorphism between ;Next we show that the sequence of diagonals produced by any Jacobi-type method that uses a sequence of sorting, diagonalizing similarities (2 x 2, 4 x 4, or even k x k) on a symmetric matrix, converges to a point in...