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Xavier Holt edited subsection_Prior_for_Weights_In__.tex
over 8 years ago
Commit id: 506fd933fe16409b1eccac78aafba9b16ccf7977
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\begin{lem}[Diagonal Matrices]
\begin{enumerate}
\item
the 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 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 For all matrices with well defined inverse and roots $A^{-1/k}=(A^{1/k})^{-1} = (A^{-1})^{1/k}$.
\end{enumerate}
\end{lem}