>> Dx=spdiags([e 2*e e], -1:1, Nx,Nx)/(dx)^{2}
Undefined operator '^' for input arguments of type 'cell'.
What is wrong with this line? cant figure it out.
MATLAB: Spdiags command not working
diagonalmatrix
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Hi Marco,
You seem to be confusing two terms: A matrix M is idempotent if 
; it's orthogonal if 
, which is what you are testing for in your code.
; it's orthogonal if , which is what you are testing for in your code.There is an orthogonal basis of eigenvectors for a matrix A if it's symmetric. In your code you're constructing a symmetric matrix, a2, but the matrix a which you're passing to eig is not symmetric.
If A is symmetric, and has two eigenpairs 
, 
, with c not equal to c, then x and y must be orthogonal:
, , with c not equal to c, then x and y must be orthogonal:
Since c and d are not equal, this implies that 
must be equal to zero, meaning that x and y are orthogonal.
must be equal to zero, meaning that x and y are orthogonal.s=0.12;N_r=30;r=linspace(0,1,N_r)';dr=r(2);r_plus=r+0.5*dr;r_minus=r-0.5*dr;a_plus=s*r_plus(1:end-1).^2;a_minus=s*r_minus(1:end-1).^2;a=-(r.^2+s*(r_plus.^2+r_minus.^2));D=[[a_minus(:);0], a(:), [0;a_plus(:)]]; %<---changed
B=spdiags(D,-1:1,N_r,N_r); %<--changed
B(1,1)=-1;B(1,2)=1;B(N_r,N_r-1)=s*(r_plus(N_r)^2+r_minus(N_r)^2);
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