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If you want to perform a PCA, I guess that using SVD will always work. Eigendecomposition on the covariance matrix only works when your data is not high dimensional(so n > p). But I'm wonder if there are circumstances in practice where you would prefer eigendecompostion over SVD?

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marked as duplicate by amoeba, gung, kjetil b halvorsen, whuber Dec 24 '14 at 1:14

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  • $\begingroup$ What is a "use case"? $\endgroup$ – Nick Cox May 7 '14 at 17:54
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    $\begingroup$ Normally "$n$" refers to the number of cases and "$p$" to the number of variables--the "dimension" of the data. Thus the high-dimensional case would ordinarily be understood as $p\gg n,$ rather than $n\gt p.$ $\endgroup$ – whuber May 7 '14 at 17:57
  • $\begingroup$ @NickCox I am not sure since I do not know when you would prefer to use it. Maybe it's computationally more efficient? $\endgroup$ – statastic May 8 '14 at 4:28
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    $\begingroup$ I don't know what you mean by the words "use case". I guess "usecase" is a typo for "use case", but the doubt remains. Perhaps you mean: are there circumstances in practice where ...? $\endgroup$ – Nick Cox May 8 '14 at 8:18
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    $\begingroup$ stats.stackexchange.com/q/79043/3277 is what you might want to read. The short answer: both work equivalently (no, you are not right saying that eigen-decomposition is for n>p only), however eigen is generally faster (if n>p) and svd is just slightly more precise. $\endgroup$ – ttnphns May 14 '14 at 19:01

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