A Geometric Framework for Non-Unitary Joint Diagonalization of Complex Symmetric Matrices

Non-unitary joint diagonalization of complex symmetric matrices is an important technique in signal processing. The so-called complex oblique projective (COP) manifold has been shown to be an appropriate manifold setting for analyzing the problem and developing geometric algorithms for minimizing the off-norm cost function. However, the recent identification of the COP manifold as a collection of rank-one orthogonal projector matrices is not a suitable framework for the reconstruction error function due to its large memory requirement compared to the actual dimension of the search space. In this work, we investigate the geometry of the COP manifold as a quotient manifold, which allows less memory requirement, and develop a conjugate gradient algorithm to minimize the reconstruction error function.