On a Matrix Algebra Related to the Discrete Hartley Transform

A new matrix algebra $\mathcal{H}$, including the set of real symmetric circulant matrices, is introduced. It is proved that all the matrices of $\mathcal{H}$ can be simultaneously diagonalized by the similarity transformation associated to the discrete Hartley transform. An application of this result to the solution of Toeplitz systems by means of the preconditioned conjugate gradient method is presented. A new matrix algebra $\mathcal{H}$, including the set of real symmetric circulant matrices, is introduced. It is proved that all the matrices of $\mathcal{H}$ can be simultaneously diagonalized by the similarity transformation associated to the discrete Hartley transform. An application of this result to the solution of Toeplitz systems by means of the preconditioned conjugate gradient method is presented.