What about returning list(T., Z) or list(quT, Z), where T. or quT is quasi-upper triangular and Z is orthogonal, consistent with the documentation? This would make it easier for people like me to build an intuition for its properties by playing with it. If it finds substantial use, someone may later suggest a special storage format for the quasi-upper-triangular part.
Thank for your work on this. Spencer Graves
Douglas Bates wrote:
Spencer Graves wrote:
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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