bdiag - block diagonalization, generalized eigenvectors
[Ab [,X [,bs]]]=bdiag(A [,rmax])
performs the block-diagonalization of matrix A . bs gives the structure of the blocks (respective sizes of the blocks). X is the change of basis i.e Ab = inv(X)*A*X is block diagonal.
rmax controls the conditioning of X ; the default value is the l1 norm of A .
To get a diagonal form (if it exists) choose a large value for rmax ( rmax=1/%eps for example). Generically (for real random A) the blocks are (1x1) and (2x2) and X is the matrix of eigenvectors.
//Real case: 1x1 and 2x2 blocks a=rand(5,5);[ab,x,bs]=bdiag(a);ab //Complex case: complex 1x1 blocks [ab,x,bs]=bdiag(a+%i*0);ab