If the numbers 1.5 and 0.5 in the brief program below were both equal to 1, it would generate the standard 7-point large sparse discretization of the Laplace operator in three dimensions. With the numbers 1.5 and 0.5 as written, we get a highly nonnormal matrix with the same sparsity pattern. A matrix like this might arise in the discretization of a convection-diffusion problem.
I = speye(N-1);
D = N^2*toeplitz([-2 1.5 zeros(1,N-3)],[-2 .5 zeros(1,N-3)]);
A = kron(I,kron(I,D)) + kron(I,kron(D,I)) + kron(D,kron(I,I));
EigTool EigTool Demos Menu.