deletions | additions       diff --git a/subsection_Prior_for_Weights_In__.tex b/subsection_Prior_for_Weights_In__.tex  index 6c9fa73..7ea9b02 100644  --- a/subsection_Prior_for_Weights_In__.tex  +++ b/subsection_Prior_for_Weights_In__.tex 
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$$p(\mathbf{w} | \boldsymbol{\sigma}) = (2\pi )^{-\frac{d}{2}} | \Sigma | ^{-\frac{1}{2}} \exp(-\frac{1}{2} \mathbf{w^T} \Sigma ^{-1} \mathbf{w})$$  \begin{lem}\label{Diagonal Matrices} \begin{lem}[Diagonal Matrices]  \begin{itemize} \begin{enumerate}  \item the inverse of a diagonal matrix is readily computable as $(\text{diag}(a_1, a_2,\dots))^{-1} = \text{diag}(a_1^{-1}, a_2^{-1}\dots) $  \item the roots of a diagonal matrix are similarly trivial with $(\text{diag}(a_1, a_2,\dots))^{1/k} = \text{diag}(a_1^{1/k}, a_2^{1/k},\dots)$  \item for all matrices with well defined inverse and roots $A^{-1/k}=(A^{1/k})^{-1} = (A^{-1})^{1/k}$.  \end{itemize} \end{enumerate}  \end{lem}