Jacobi Angles for Simultaneous Diagonalization

. Simultaneous diagonalization of several matrices can be implemented by a Jacobi-like technique. This note gives the required Jacobi angles in close form. Key words. Simultaneous diagonalization, Jacobi iterations, eigenvalues, eigenvectors, structured eigenvalue problem. AMS subject classifications. 65F15, 65-04. Introduction. Simultaneous diagonalization of several commuting matrices has been recently considered in 1, mainly motivated by stability and convergence concerns. Exact or approximate simultaneous diagonalization was also independently introduced as a solution to a statistical identification problem 2 (see 3 for a later paper in English). The simultaneous diagonalization algorithm described in these papers is an extension of the Jacobi technique: a joint diagonality criterion is iteratively optimized under plane rotations. The purpose of this note is to complement 1 by giving a close form expression for the optimal Jacobi angles. 1. Jacobi angles in close form. C...