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Scilab help >> Linear Algebra > bdiag


block diagonalization, generalized eigenvectors

Calling Sequence

[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


[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*Xis 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

//Complex case: complex 1x1 blocks

See Also

  • schur — [ordered] Schur decomposition of matrix and pencils
  • sylv — Sylvester equation.
  • spec — eigenvalues of matrices and pencils
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Last updated:
Thu May 12 11:44:14 CEST 2011