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From this article and this post it emerges the strong connection between Mahalanobis distance and PCA. In particular in the first article I reference it says:

" the squared Mahalanobis distance is equal to the sum of squares of the scores of all non‐zero standardized principal components"

I would like to have a mathematical proof or at least some reference where I can read the proof.

Many thanks

gioxc88
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    This question is not a duplicate. In my question I also cite the topic that you mention @Sycorax says Reinstate Monica. I asked for a mathematical proof not for a "How would you explain it to your grandma"-explanation" as it's asked in the topic "Bottom to top explanation of the Mahalanobis distance?". At least take the time to read the question before closing the topic. This only demonstrates that you didn't read neither my question nor the other topic which you claim already contains an answer to my question. – gioxc88 Mar 06 '20 at 17:10
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    Scroll down to my answer, or read Whuber's note about PCA in his answer. The answers directly address the core of your query. – Sycorax Mar 06 '20 at 17:31
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    https://stats.stackexchange.com/a/261248/40036 answers your question, though (one of the answers in the marked duplicate). – josliber Mar 06 '20 at 17:31
  • @SycoraxsaysReinstateMonica thank you !!!! – gioxc88 Mar 06 '20 at 22:23

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