deletions | additions       diff --git a/subsubsection_Principal_Component_Analysis_We__.tex b/subsubsection_Principal_Component_Analysis_We__.tex  index 0cd6f48..08af5fa 100644  --- a/subsubsection_Principal_Component_Analysis_We__.tex  +++ b/subsubsection_Principal_Component_Analysis_We__.tex 
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\subsubsection{Principal Component Analysis}  We present Principle component analysis (PCA) determines a set of orthogonal axes that maximize  the velocity channel covariance matrices variance  of runs W1T2t0.2 the data. As applied to spectral data cubes, it identifies differences between the line profiles,  and W2T2t0 in Figure 3. Multiple covariances of velocity channels thus, is a useful tool for distinguishing  between -2 kinematic changes  and 2 km/s are larger in run W1T2t0.2 than those in run W2T2t0. There appears to be distinct peaks at noise \citep{heyer97,heyer02}. First, a 2-D covariance matrix is constructed from  the center of both matrices. We find that feedback augments spectra. Next, the eigenvalues  and further separates these peaks. This corresponds eigenvectors of this matrix are determined. Here, we use the eigenvalues  to assess  the typical expansion rate degree  of the wind shells. difference between two datasets.  Figure 3 shows the velocity channel covariance matrices of runs W1T2t0.2 and T2t0. Both runs show a signal for velocities $|v| \lessim 2 \kms$, which roughly encompases the range of velocity dispersions in the turbulent gas. 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 when winds are present. 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}.  (This appears to, so far, be the only statistic that I don't give much background on. I feel as if the PCA is more about obtaining the eigenbasis for the covariance matrix than it is about the actual covariance matrix. Here, we only look at the covariance matrix. The distance metrics table uses the eigenvalues, so I'm thinking of mentioning some of the PCA background there. I just find it kind of ironic that on this section appears to have one of the most interesting changes while being one of the shortest sections) -> We may need to provide plots of the eigenvalues.