Nonnormal upwind amplification matrix
= Nonnormal upwind amplification matrix
On a finite inflow grid, explicit upwinding has a triangular amplification matrix whose only eigenvalue is $1-\mu$. For $1<\mu<2$ this eigenvalue lies inside the unit disk, although interior high-frequency data are amplified by $|1-2\mu|>1$ before reaching the boundary. This shows why eigenvalue analysis without uniform normality can give the wrong stability range.