Joint diagonalization of non defective matrices using generalized Jacobi rotations

This paper addresses the problem of joint diagonalization (JD) of a set of non defective matrices. A new Jacobi-like method that has the advantages of fast and efficient computation as well as generality is presented. The proposed algorithm uses a combination of unitary and shear (non unitary) transformations to bring general matrices into normal ones and perform joint diagonalization. This algorithm is named JUST for Joint Unitary Shear Transformation. A comparison with another general algorithm, namely the FFDiag is provided and the overall algorithm performance is assessed and discussed through numerical simulations.