Comments on: The Jordan Canonical Form Just Doesn’t Compute https://blogs.mathworks.com/cleve/2018/05/28/the-jordan-canonical-form-just-doesnt-compute/?s_tid=feedtopost Cleve Moler is the author of the first MATLAB, one of the founders of MathWorks, and is currently Chief Mathematician at the company. He writes here about MATLAB, scientific computing and interesting mathematics. Thu, 14 Jun 2018 23:08:35 +0000 hourly 1 https://wordpress.org/?v=6.2.2 By: Cleve Moler https://blogs.mathworks.com/cleve/2018/05/28/the-jordan-canonical-form-just-doesnt-compute/#comment-6574 Thu, 14 Jun 2018 23:08:35 +0000 https://blogs.mathworks.com/cleve/?p=3401#comment-6574 In reply to Steve Lord.

Thanks very much, Steve. As I’ve said in this blog before, John Todd was the Caltech professor who got me started in this business. But that still doesn’t tell us who T. S. Wilson was.
— Cleve

]]>
By: Steve Lord https://blogs.mathworks.com/cleve/2018/05/28/the-jordan-canonical-form-just-doesnt-compute/#comment-6572 Thu, 14 Jun 2018 21:55:26 +0000 https://blogs.mathworks.com/cleve/?p=3401#comment-6572 Tahar Loulou,

A quick Google search found a paper titled “APPLICATION OF THE CONCEPT OF THE CONDITIONING OF A MATRIX TO AN IDENTIFICATION PROBLEM” by Jacques Delforge in “Comp. and Maths with Appls. Vol. 4 pp. 139-148” that has a matrix very similar to the one you posted (the first and second columns were interchanged.) The paper says this example was due to T. S. Wilson and quoted by Bodewig and Todd.

It appears in the form you quoted on page 134 of Bodewig’s “Matrix Calculus” and with the interchanged columns as an exercise on page 48 of Todd’s “Basic Numerical Mathematics: Vol 2: Numerical Algebra” according to Google Books.

]]>
By: Cleve Moler https://blogs.mathworks.com/cleve/2018/05/28/the-jordan-canonical-form-just-doesnt-compute/#comment-6546 Sat, 09 Jun 2018 20:25:18 +0000 https://blogs.mathworks.com/cleve/?p=3401#comment-6546 In reply to Tahar Loulou.

Thank you for the comment, Tahar.
The matrix looks familiar, but I can’t remember where I saw it. I have never used it myself.
Its condition is only 2.9841e+03.
I’m afraid I have no idea who T. S. Wilson is, or was. I don’t recognize that name at all.
— Cleve

]]>
By: Tahar Loulou https://blogs.mathworks.com/cleve/2018/05/28/the-jordan-canonical-form-just-doesnt-compute/#comment-6544 Sat, 09 Jun 2018 19:29:11 +0000 https://blogs.mathworks.com/cleve/?p=3401#comment-6544 Dear Professor Moler,

The last year you have published the following post :
What is the Condition Number of a Matrix?
Posted by Cleve Moler, July 17, 2017

In many books on numerical analysis, there is a famous matrix that is presented all the time
when the authors deal with the cond number of matrix. They use the example due to T. S. Wilson where
the matrix A = [5 7 6 5; 7 10 8 7; 6 8 10 9; 5 7, 9 10], x = [1; 1; 1; 1]; and b = [32 23 33 31]. In Matlab language :
A.x = b.
Please could you give us more information on this author and the origin of this matrix.
Any bibliographic reference about this author is welcome.

Thank you very much.
Thank you aslo for Matlab software, it genious tool.

]]>