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I'm currently reading the paper about eigenfaces. Sadly I can't follow the first step to calculation the eigenfaces.

\begin{align} C & = \frac{1}{M}\sum_{n=1}^{M}{\Phi_n\Phi_n^T} =AA^T \end{align} Where $\Phi_i = \Gamma_i -\Psi$ and $\Gamma_i$ is one image rearranged into one vector and $\Psi$ is the average of all images and $A = [ \Phi_0,\Phi_1,...,\Phi_M]$

Can someone explain the intermediate steps to me?

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up vote 0 down vote accepted

There's an error both in the paper and in your rendition of it. In the paper it says $A = [ \Phi_1,...,\Phi_M]$; there's no $\Phi_0$. And the factor $1/M$ is missing in the paper on the right-hand side. So the correct equation is

$$C=\frac1M\sum_{n=1}^M\Phi_n\Phi_n^T =\frac1MAA^T\;.$$

Hope that clears things up.

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But will the part $1/M$ contribute any information other than a scaling factor. Just for knowing, since I am a beginner. I have seen many works on PCA directly starting from $\bf{AA^T}$. – dexterdev May 11 '14 at 6:52

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