For anyone curious about the rounding error in the skew-symmetric tridiagonal matrices eigenvalue plot. This shows a close up of the rounding error (a different family of matrices but the same principle applies).
The red circles have radii of eps^(1/m) (machine epsilon) giving the expected rounding error for eigenvalues of multiplicity m in double precision with m=15 for the outermost circle.
The family used here is 20x20 "anti-tridiagonal" matrices (an upside-down tridiagonal matrix) with population {-1, 0, 1}. 100 million matrices were sampled.
Today's @BohemianMatrix computation, by my student Aaron Asner: the eigenvalues of all 31 by 31 skew-symmetric tridiagonal matrices with population 1 and i. Over a billion matrices; computation in parallel on a 64 core machine took 85 hours. The center rose is rounding error!
The work (with @stevejtrettel and Kate Stange) I have been trailing for a while on Algebraic number starscapes (the patterns in polynomial roots) is now up on the arXiv; arxiv.org/abs/2008.07655 It is a math paper, but the images should be accessible to all!
ALT Eigenvalue density plot for all 13 by 13 complex symmetric tridiagonal matrices with zero main diagonal and population 1, exp(I*pi/4), and its conjugate. Colorized to make art. Well, perhaps it's art.
Ok enough about other people's talks. I'm giving two: one Thursday, a general introduction to Maple @maplesoft and one Friday where I will show how to make @BohemianMatrix pictures like this in Maple.
In my upcoming (Dec 12/13) masterclass in Maple @NewtonInstitute, participants will learn how to make @BohemianMatrix pictures like this. This is hybrid symbolic numeric computation. @maplesoft [5th roots of unity, 7 by 7 symmetric tridiagonal 0 main diagonal]