MATLAB Mathematics - SERC - Index of

Eigenvalues
Schur Decomposition in MATLAB Matrix Computations
The MATLAB advanced matrix computations do not require eigenvalue
decompositions. They are based, instead, on the Schur decomposition
A = U S U T
where U is an orthogonal matrix and S is a block upper triangular matrix with
1-by-1 and 2-by-2 blocks on the diagonal. The eigenvalues are revealed by the
diagonal elements and blocks of S, while the columns of U provide a basis with
much better numerical properties than a set of eigenvectors. The Schur
decomposition of this defective example is
[U,S] = schur(A)
U =
-0.4741 0.6648 0.5774
0.8127 0.0782 0.5774
-0.3386 -0.7430 0.5774
S =
-1.0000 20.7846 -44.6948
0 1.0000 -0.6096
0 0 1.0000
The double eigenvalue is contained in the lower 2-by-2 block of S.
Note If A is complex, schur returns the complex Schur form, which is upper
triangular with the eigenvalues of A on the diagonal.
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