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Why would PCs be in the same direction as the axes of ellipsoid if they are our right singular vectors in SVD?

This story is from 2026-09-16. It is preserved in the archive; the latest stories are on the live feed.

We know that in SVD, the right singular vectors are actually PRE-IMAGES of the axes of ellipsoids. But PCs are said to be the axes themselves. Aren't PCs supposed to be in the same direction as right singular vectors?

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  1. 2026-09-16 13:54 · r/learnmachinelearning
    Why would PCs be in the same direction as the axes of ellipsoid if they are our right singular vectors in SVD?

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