Does R have a function for the Schur decomposition? The documentation for library(Matrix) describes a function "Schur", but it seems to be missing from the Windows version 0.8-14 (2004-09-14) and 0.8-15 (2004-10-02).
The R 2.0.0 pat documentation for "eigen" refers to "http://www.netlib.org/lapack/lug/lapack_lug.html";, and the description there for eigen analysis of a non-symmetric matrix says, "This problem can be solved via the Schur factorization of A, defined in the real case as
A = ZTZT,
where Z is an orthogonal matrix and T is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal blocks, the 2-by-2 blocks corresponding to complex conjugate pairs of eigenvalues of A."
Thanks,
Spencer Graves
That documentation entry was a note to myself to add the Schur factorization to the Matrix package but I have not yet done so. If anyone can suggest a reasonable data structure for the result, it would be fairly easy to add the Schur decomposition.
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