Bohemian Matrices

The family used here is 20x20 "anti-tridiagonal" matrices (an upside-down tridiagonal matrix) with population {-1, 0, 1}. 100 million matrices were sampled.

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.

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).

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!

It's a @BohemianMatrix book! But not by name ;)

Just in time for February, the 2021 Bohemian Matrices calendar is ready thanks to @corless_rob. Download your copy at bohemianmatrices.com.

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!

Happy to announce that our Generalized Standard Triples paper (a part of the @BohemianMatrix Project) has been revised. Thanks @LeiliRafiee and @euniceyschan and to @tisseurf for the feedback! arxiv.org/abs/1805.04488

"Electric Bohemian 13" my last @BohemianMatrix image done @NewtonInstitute for 2019. Thanks @maplesoft and @3j0hn for the Color Tools package.

Ok I'm happy with this @BohemianMatrix picture. Merry Newtonmas! Come to my @NewtonInstitute masterclass to learn how to use Maple to make your own. @maplesoft

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]

Currently designing my masterclass in Maple for #NewtonCAT219 at @NewtonInstitute next month. Naturally, @BohemianMatrix gets a showing. I think people may enjoy building their own. @maplesoft @westernuAPMaths @rotmanphilo

Congratulations to Dr @euniceyschan !! The newest PhD in @westernuAPMaths and @rotmanphilo ! Thanks to @tisseurf for being the external examiner :)

Cleve explaining the Moler matrix at @BohemianMatrix minisymposium at @ICIAM2019

Gil Strang going strong @ICIAM2019 at our @BohemianMatrix minisymposium meeting some old and new @westernuAPMaths friends!

Here is @euniceyschan giving her talk at the @BohemianMatrix minisymposium @westernuAPMaths @rotmanphilo

MATLAB's creator Cleve Moler will be taking part at the minisymposium on "Bohemian Matrices" at @ICIAM2019 on Friday 19. Do not miss it! @MathWorks #weloveMATLAB SPOILER AHEAD 👇🧐⚠️ blogs.mathworks.com/cleve/2019/06/…