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bdiag

bdiag — block diagonalization, generalized eigenvectors

Calling sequence

[Ab [,X [,bs]]]=bdiag(A [,rmax])

Parameters

A : real or complex square matrix
rmax : real number
Ab : real or complex square matrix
X : real or complex non-singular matrix
bs : vector of integers

Description



[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.

Examples



//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

See also

schur, sylv, spec
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