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It isn't very clear to me what distances you are trying to compute. PCA is frequently described as dropping the smallest elements and retaining the k major elements. So any length you compute in that k-dimensional Place is really an approximation of distance in the first facts.
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Probably you can uncover it in a textbook that discusses Hotelling's you could look here T^2 statistic, which makes use of a similar computation. If you can't come across it in print, you'll be able to constantly cite my web site, which has been cited in lots of textbooks, papers, and in some cases by Wikipedia.
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If you change the scale within your variables, then the covariance matrix also adjustments. In case you evaluate MD by utilizing the new covariance matrix to evaluate The brand new (rescaled) facts, you get exactly the same respond to as if you utilized the initial covariance matrix to evaluate the first facts.
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