[jira] [Created] (MATH-1645) EigenDecomposition returns eigenvalues/vectors IN ORDER?

["Richard K Belew (Jira)" <ji...@apache.org>]

Richard K Belew created MATH-1645:
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             Summary: EigenDecomposition returns eigenvalues/vectors IN ORDER?
                 Key: MATH-1645
                 URL: https://issues.apache.org/jira/browse/MATH-1645
             Project: Commons Math
          Issue Type: Improvement
    Affects Versions: 3.6.1
            Reporter: Richard K Belew


It appears that getRealEigenvalues() and getEigenvector() return values in decreasing order of eigenvalues (largest first)?  This would be a good feature to reveal in the `org.apache.commons.math4.linear.EigenDecomposition.java` documentation.

I propose adding this simple sentence:

> The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.multiply(V) equals V.multiply(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon the condition of V.

The eigenvalues returned by getRealEigenvalues() and eigenvectors returned by getEigenvector() are in decreasing order of eigenvalues (largest first).

> This implementation is based on the paper by A. Drubrulle, R.S. Martin and J.H. Wilkinson "The Implicit QL Algorithm" in Wilksinson and Reinsch (1971) Handbook for automatic computation, vol. 2, Linear algebra, Springer-Verlag, New-York.

(I've not tried to patch within the Commons framework, or I'd produce a pull request.)



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