One-Dimensional Euler Equations
(Eigensystem of A=dF/dU)

    ==                   ==
    |                     |
    |  u      0       0   |
    |                     |
L = |  0     u+c      0   |
    |                     |
    |  0      0      u-c  |
    |                     |
    ==                   ==
 
 

    ==                                                              ==
    |                                                                |
    |   -1/c         1/c                      -1/c                   |
    |                                                                |
T = |   -u/c         1 + u/c                   1 - u/c               |
    |                                                                |
    |   -u2/(2c)     u + c/(g-1) + u2/(2c)      u - c/(g-1) - u2/(2c) |
    |                                                                |
    ==                                                              ==
 
 

      ==                                                                      ==
     |  [(g-1)/(2c)][u2 - 2c2/(g-1)]  -(g-1)u/c                    (g-1)/c     |
     |                                                                         |
T-1 = |  [(g-1)u/(4c)][u - 2c/(g-1)]   -[(g-1)/(2c)][u - c/(g-1)]   (g-1)/(2c)  |
     |                                                                         |
     | -[(g-1)u/(4c)][u + 2c/(g-1)]    [(g-1)/(2c)][u + c/(g-1)]  -(g-1)/(2c)  |
     |                                                                         |
      ==                                                                      ==