bdiag

Arguments

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*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.

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 — [ordered] Schur decomposition of matrix and pencils
• sylv — Sylvester equation.
• spec — eigenvalues of matrices and pencils
• blockdiag — Создаёт блочную диагональную матрицу из указанных массивов. Соединение диагональной системы блоков.