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bdiag(2) Scilab Function bdiag(2)
NAME
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.
EXAMPLE
//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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