deletions | additions       diff --git a/subsubsection_Principal_Component_Analysis_Principle__.tex b/subsubsection_Principal_Component_Analysis_Principle__.tex  index 24549b1..e064415 100644  --- a/subsubsection_Principal_Component_Analysis_Principle__.tex  +++ b/subsubsection_Principal_Component_Analysis_Principle__.tex 
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Figure 3 shows the velocity channel covariance matrices of runs W1T2t0.2 and T2t0. Both runs show a signal for velocities $|v| \lesssim 2 \kms$, which roughly encompasses the range of turbulent gas velocities. However, W1T2t0.2 exhibits multiple strong covariance peaks around a few $\kms$. These features exist to a lesser degree for T2t0, but feedback augments and further separates the peaks. The strongest covariance corresponds to the typical expansion rate of the wind shells.  Because the eigenvectors provide a measure of the strength of different eigenvectors, they also serve as a proxy of the amount of power on different scales \citep{brunt08}. Figure \ref{eigenvalue} shows the relative sizes of the largest eigenvalues. Our algorithm calculates the first 50 and uses these to determine the degree of difference between two datacubes. However, only the first ten are significant. For observations, eigenvalues beyond the first 10 are dominated by noise.  We find a clear difference in the eigenvalues for the cases with and without feedback. The case with feedback has more significant second, third and fourth eigenvalues. This is likely due to the additional emission structure created by the winds. %Ask Mark about PCA and feedback -- Brunt et al. 2003 paper analyzed simualtions with point expostions? but no break