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I have a set of data that has $n$ samples described by $m$ variables. I do a PCA to reduce it to just 2 dimensions. I understood that what I did is basically $$\mathrm{PC}=VX,$$ where $\mathrm{PC}$ are the principal components, $X$ is the original matrix with the data (centered, and with data points in columns) and $V$ is the matrix with the loadings (the matrix with the eigenvectors of the sample covariance matrix of $X$).

Now my question is : If I have 2 PCs, is there any way that I can retrieve the original data (in the original dimensions) without any prior information on the information included in $X$, so without using the matrix $V$?

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    $\begingroup$ ______No______. $\endgroup$ – amoeba Jun 9 '15 at 7:38

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