To my knowledge, the Jacobian matrix A for the 1D shallow water equations is
|0 1 |
|-u^2 + g * h 2*u|
that is known to give the eigenvalues such as
Lamba1 = u - sqrt(9.81 * h)
Lamba2 = u + sqrt(9.81 * h)
Now, let's assume the values as follows:
h = 1
u = 2
Lamba1 = u - sqrt(9.81 * h) = 2 - sqrt(9.81 * 1) = -3.13
Lamba2 = u + sqrt(9.81 * h) = 2 + sqrt(9.81 * 1) = +3.13
If the identity matrix I is
|1 0|
|0 1|
My question is then: why is NEITHER det|A - Lambda1 x I| NOR det|A - Lamba2 x I| equal zero? Have I misunderstood the concept here?
Any advices would be appreciated. Thank you.