Schur decomposition
T = schur(A)
T = schur(A,flag)
[U,T] = schur(A,...)
The schur function computes the Schur form of a matrix.
T = schur(A) returns the
Schur matrix T.
T = schur(A,flag) for real
matrix A, returns a Schur matrix T in one of two
forms depending on the value of flag:
'complex' |
|
'real' |
|
If A is complex, schur returns
the complex Schur form in matrix T and flag is
ignored. The complex Schur form is upper triangular with the eigenvalues
of A on the diagonal.
The function rsf2csf converts the real Schur
form to the complex Schur form.
[U,T] = schur(A,...) also
returns a unitary matrix U so that A =
U*T*U' and U'*U = eye(size(A)).
H is a 3-by-3 eigenvalue test matrix:
H = [ -149 -50 -154
537 180 546
-27 -9 -25 ]Its Schur form is
schur(H)
ans =
1.0000 -7.1119 -815.8706
0 2.0000 -55.0236
0 0 3.0000The eigenvalues, which in this case are 1, 2,
and 3, are on the diagonal. The fact that the off-diagonal
elements are so large indicates that this matrix has poorly conditioned
eigenvalues; small changes in the matrix elements produce relatively
large changes in its eigenvalues.