diff --git a/report.tex b/report.tex index 94a3eae..3d14c79 100644 --- a/report.tex +++ b/report.tex @@ -248,7 +248,7 @@ where both $A$ and $S$ can depend on $u^I$ but not their derivatives. For any unit covector $\xi_i$, the \emph{Principal symbol} matrix is defined as $\tensor{P}{^I_J}(\xi) := \tensor{A}{^i^I_J} \xi_i$. The system is said to be: \begin{itemize} - \item \emph{weekly hyperbolic} if for any $\xi_i$, $\tensor{P}{^I_J}(\xi)$ has only real eigenvalues. + \item \emph{weakly hyperbolic} if for any $\xi_i$, $\tensor{P}{^I_J}(\xi)$ has only real eigenvalues. \item \emph{strongly hyperbolic} if for any $\xi_i$, $\tensor{P}{^I_J}(\xi)$ has only real eigenvalues and a complete set of eigenvectors, i.e., it is diagonalizable. \item \emph{symmetrically hyperbolic} if there exists a positive definite symmetrizer matrix $H_{IJ}$ such that $H_{IK} \tensor{P}{^K_J}(\xi)$ is always symmetric. \end{itemize}