diff --git a/report.tex b/report.tex index bb67d56..786cd91 100644 --- a/report.tex +++ b/report.tex @@ -289,16 +289,15 @@ it's very clear that the principal symbol matrix is already symmetric, and thus the system is symmetrically hyperbolic, and well-posed in the $L^2$ sense. The eigenvalues are $\lambda_1 = \lambda_2 = \lambda_3 = 0$, $\lambda_4 = -1$ and $\lambda_5 = 1$. The eigenvectors are - { - % \fontsize{small} \begin{equation} - \myvec{e}_1 = \mqty(1,0,0,0,0)^T, - \myvec{e}_2 = \mqty(0,0,-\xi_3,0,\xi_1)^T, - \myvec{e}_3 = \mqty(0,0,-\xi_2,\xi_1,0)^T, - \myvec{e}_4 = \mqty(0,1,\xi_1,\xi_2,\xi_3)^T, - \myvec{e}_5 = \mqty(0,-1,\xi_1,\xi_2,\xi_3)^T. + \begin{split} + \myvec{e}_1 = \mqty(1,0,0,0,0)^T,\\ + \myvec{e}_2 = \mqty(0,0,-\xi_3,0,\xi_1)^T,\\ + \myvec{e}_3 = \mqty(0,0,-\xi_2,\xi_1,0)^T,\\ + \myvec{e}_4 = \mqty(0,1,\xi_1,\xi_2,\xi_3)^T,\\ + \myvec{e}_5 = \mqty(0,-1,\xi_1,\xi_2,\xi_3)^T. + \end{split} \end{equation} - } \end{frame}