Lowdin正交化的中心性
Centrality of Lowdin orthogonalizations
摘要：
给出了Lowdin正交化中存在的不同正交关系。其他正交化技术，如极分解（PD），主成分分析（PCA）和减少奇异值分解（SVD）可以从Lowdin方法。分析表明，极分解是在对称正交化下进行的，主成分分析和奇异值分解是在正则正交化下进行的。正则正交化可以转化为约化SVD的形式，反之亦然。建立了对称正交化方法与标准正交化方法之间的解析关系。给出了对称正交化与奇异值分解的内在联系。
英文摘要：
The different orthogonal relationships that exists in the Lowdin orthogonalizations is presented. Other orthogonalization techniques such as polar decomposition (PD), principal component analysis (PCA) and reduced singular value decomposition (SVD) can be derived from Lowdin methods. It is analytically shown that the polar decomposition is presented in the symmetric orthogonalization; principal component analysis and singular value decomposition are in the canonical orthogonalization. The canonical orthogonalization can be brought in into the form of reduced SVD or vice-versa. The analytic relation between symmetric and canonical orthogonalization methods is established. The inter-relationship between symmetric orthogonalization and singular value decomposition is presented.
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