Singular Value Decomposition and the Centrality of Löwdin Orthogonalizations
نویسنده
چکیده
The different orthogonal relationship that exists in the Löwdin orthogonalizat ions is presented. Other orthogonalizat ion techniques such as polar decomposition (PD), principal component analysis (PCA) and reduced singular value decomposition (SVD) can be derived from Löwdin methods. It is analytically shown that the polar decomposition is presented in the symmetric o rthogonalization; principal component analysis and singular value decomposition are in the canonical orthogonalization. The canonical orthogonalizat ion can be brought into the form of reduced SVD or vice-versa. The analytic relation between symmetric and canonical orthogonalizat ion methods is established. The inter-relationship between symmetric o rthogonalization and singular value decomposition is presented.
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