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Description: _ Okamoto(2006) (see the file okamoto_2006.pdf in the Files box below) explains principal components analysis (PCA) from the point of view of orthogonal projection. Choice of the bases in the projected space is arbitrary, that is, rotation of the basis is allowed. Deisenroth et al. (2006) also explains PCA in terms of an orthonormal projection. The equivalence of these two methods is shown in the file TwoCriterions.pdf in the Files box below. The proof in Appendix of Okamoto(2006), which derives the orthogonal projection, may be extended to an infinite dimensional space. Python scripts for PCA, which gives rotated components, are included in the archived file pcafiles.zip with the readme.pdf. _ A simple explanation of the projective method was presented at https://OSF.IO/76GC9 _ Reference Deisenroth, M. P., Faisal, A. A., & Ong, C. S. (2020). Mathematics for machine learning. Cambridge University Press. Okamoto,Y. (2006). A justification of rotation in principal component analysis: Projective viewpoint of PCA. Japan Women’s University Journal: Faculty of Integrated Arts and Social Sciences Journal,17, 59-71. _