Eigenvalues in PCA When I carry out Principal Component Analysis, the outputs are the Eigen-values and Eigen-vectors for each PC.
Question: are the Eigen-values directly proportional to the Variance explained by the PC? For example, for a three-dimensional data-set, my Eigen-values came out as: 0.007, 0.002, 0.001. Does that mean that the first PC captures 0.007 / (0.007 + 0.002 + 0.001) ~ 77% of the variance?

There are 2 concepts to look out for and it can get confusing at first. Let me put it the best way you can understand:

*

*Variance of one PC:
The variance for the $i^{th}$ principal component is equal to the $i^{th}$ Eigenvalue. In your case, the variance of the $1^{st}$ PC is equal to the $1^{st}$ Eigenvalue which is 0.007.


*Proportion of Variance by one PC:
The proportion of variation explained by the $i^{th}$ principal component is then defined to be the eigenvalue for that component divided by the sum of the eigenvalues. In other words, the $i^{th}$ principal component explains the proportion of the total variation for total number of factors let's say $n$ as:
$x_i$/$\sum$$x_{i\to{n}}$
Your interpretation is the 2nd one which explains the proportion of variance captured.

If you divide the $1^{st}$ PC by the sum of all EVs, you will get the proportion of variance captured.
Hope this helps!
