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.TH bdiag 2 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
bdiag - block diagonalization, generalized eigenvectors
.SH CALLING SEQUENCE
.nf
[Ab [,X [,bs]]]=bdiag(A [,rmax])
.fi
.SH PARAMETERS
.TP
A
: real or complex square matrix
.TP 6
rmax
: real number
.TP 3
Ab
: real or complex square matrix
.TP 2
X
: real or complex non-singular matrix
.TP 3
bs
: vector of integers
.SH DESCRIPTION
.nf
[Ab [,X [,bs]]]=bdiag(A [,rmax])
.fi
performs the block-diagonalization of matrix \fVA\fR.
bs gives the structure of the blocks (respective sizes of the blocks).
\fVX\fR is the change of basis i.e
.Vb Ab = inv(X)*A*X
is block diagonal.
.LP
\fVrmax\fR controls the conditioning of \fVX\fR; the default value is the
l1 norm of \fVA\fR.
.LP
To get a diagonal form (if it exists) choose a large value for
\fVrmax\fR (\fVrmax=1/%eps\fR for example).
Generically (for real random A) the blocks are (1x1) and (2x2) and \fVX\fR
is the matrix of eigenvectors.
.SH EXAMPLE
.nf
//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
.fi
.SH SEE ALSO
schur, sylv, spec
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