Message-ID: <23294.36020.142442.43143@stat.math.ethz.ch>
Date: 2018-05-18T08:20:04Z
From: Martin Maechler
Subject: [R-pkg-devel] mvrnorm, eigen, tests, and R CMD check
In-Reply-To: <CAF8bMcb1LMrk3b0djs+hjemSyeSFYcmM8u70K2kbkmMmCCe6=A@mail.gmail.com>
>>>>> William Dunlap
>>>>> on Thu, 17 May 2018 11:28:50 -0700 writes:
> Your explanation needs to be a bit more general in the
> case of identical eigenvalues - each distinct eigenvalue
> has an associated subspace, whose dimension is the number
> repeats of that eigenvalue and the eigenvectors for that
> eigenvalue are an orthonormal basis for that subspace.
> (With no repeated eigenvalues this gives your 'unique up
> to sign'.)
Thank you, Bill, notably for the concrete example of non-trivial
eigenspaces (per eigenvector).
Note I did say
"... such that at least for the good cases where all eigenspaces
are 1-dimensional, ..."
knowing well that only in that case it "is easy".
I have a gut feeling but may be wrong that such simplistic post
processing may also help (to get cross-platform reproducibility)
in the case of MASS::mvrnorm() where repeated eigenvalues will
be common in practice.
Martin