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A geometric framework for non-unitary joint diagonalization of complex symmetric matrices. (English) Zbl 1406.65023

Nielsen, Frank (ed.) et al., Geometric science of information. First international conference, GSI 2013, Paris, France, August 28–30, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-40019-3/pbk). Lecture Notes in Computer Science 8085, 353-360 (2013).
Summary: 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.
For the entire collection see [Zbl 1284.94005].

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A23 Factorization of matrices
51E20 Combinatorial structures in finite projective spaces
53A20 Projective differential geometry
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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