block diagonalization, generalized eigenvectors
[Ab [,X [,bs]]]=bdiag(A [,rmax])
real or complex square matrix
real number
real or complex square matrix
real or complex non-singular matrix
vector of integers
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 | ![]() | ![]() |