1.5.3 Hyperbolic system
A linear system (43) of PDEs
is called
hyperbolic
if
is
diagonalizable,
i.e., there exists a matrix
with

(46) 
and
is in diagonal form
(with real numbers on the diagonal: the eigenvalues of
).
With the definition

(47) 
Eq. (43) gets the
characteristic form

(48) 
This is now a set of independent equations, each of the simple form

(49) 
A quasilinear system with
can be hyperbolic at point
.