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I am reading Principal Component Analysis (PCA) from Wikipedia. Under the details section, it states that the principal components are just eigenvectors of $X^T X$ where $X$ is the data matrix.

However, this post suggests that principal components are covariance matrix's eigenvectors.

I am confused now. To obtain principal components in PCA, which matrix do we use? $X^T X$ or covariance matrix of $X$?

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  • $\begingroup$ Where's the contradiction? $\endgroup$ – Rodrigo de Azevedo Apr 1 at 12:28
  • $\begingroup$ No contradiction. I am not sure which matrix to use when I want to calculate principal component. Is it data matrix or its covariance matrix? Do we get the same set of principal components for either matrix? $\endgroup$ – Idonknow Apr 1 at 12:29
  • $\begingroup$ Isn't $X^T X$ the covariance matrix? $\endgroup$ – Rodrigo de Azevedo Apr 1 at 12:30
  • $\begingroup$ Opps. I think I need to polish up my knowledge on multivariate covariance matrix. Can you give a reference on showing that $X^T X$ is the covariance matrix of $X$? $\endgroup$ – Idonknow Apr 1 at 12:33
  • $\begingroup$ Is it? I don't know. To me, this looks like asking about singular vectors and eigenvectors. $\endgroup$ – Rodrigo de Azevedo Apr 1 at 12:34

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