MATLAB Function Reference |
Convert real Schur form to complex Schur form
Syntax
Description
The complex Schur form of a matrix is upper triangular with the eigenvalues of the matrix on the diagonal. The real Schur form has the real eigenvalues on the diagonal and the complex eigenvalues in 2-by-2 blocks on the diagonal.
converts the real Schur form to the complex form. [U,T] = rsf2csf(U,T)
Arguments U
and T
represent the unitary and Schur forms of a matrix A
, respectively, that satisfy the relationships: A
= U*T*U'
and U'*U
= eye(size(A))
. See schur
for details.
Examples
Generating the Schur form of A
and converting to the complex Schur form
yields a triangular matrix T
whose diagonal (underlined here for readability) consists of the eigenvalues of A
.
U = -0.4916 -0.2756 - 0.4411i 0.2133 + 0.5699i -0.3428 -0.4980 -0.1012 + 0.2163i -0.1046 + 0.2093i 0.8001 -0.6751 0.1842 + 0.3860i -0.1867 - 0.3808i -0.4260 -0.2337 0.2635 - 0.6481i 0.3134 - 0.5448i 0.2466 T = 4.8121 -0.9697 + 1.0778i -0.5212 + 2.0051i -1.0067 0 1.9202 + 1.4742i 2.3355 0.1117 + 1.6547i 0 0 1.9202 - 1.4742i 0.8002 + 0.2310i 0 0 0 1.3474
See Also
rref | run |
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