I wish to get a better understanding of the meaning of the eigenvalues of a correlation matrix I am studying.
I have a correlation matrix of noise levels for 10 cells in a wireless network over time. Let's say I have 1000 time series points for each variable, I then normalise the time series points using a sliding window approach by subtracting the mean of the window and divide by the S.D before I create 1000 10x10 correlation matrices.
I have then calculated the eigenvalues for the each of the 4 different sized windows I have used and using the original index I can identify periods when I would expect the greatest amount of noise in the original time series actually have some of the smaller eigenvalue magnitudes.
What do these eigenvalues actually represent, I've read that the first eigenvalues explain the maximum amount of variance of the variables which can be accounted for with a linear model by a single underlying factor . But this means nothing to me right now, I understand variance and how it is a measure of spread but what a linear model is but I can't piece the two parts together intuitively.
Here is a sample plot of four variables in the original time series:
And here is a sample of the largest eigenvalues using 4 different sized windows for a 10x10 matrix
What is the translation from the time series domain to the eigenvalue spectrum?