Hyperbolicity
= Hyperbolicity
For a one-dimensional first-order system $v_t+A(v,x,t)v_x=s$, hyperbolicity means that the coefficient <matrix> has real <eigenvalues> and a complete set of <eigenvectors>. Distinct real eigenvalues give strict hyperbolicity and separate <characteristic curves>. Along a curve of speed $\lambda$, a left <eigenvector> $\ell A=\lambda\ell$ gives the compatibility equation $\ell\,dv/dt=\ell s$.