A look at the structure, and the eigenvalues and singular values of interesting test matrices.... read more >>

MATLAB has two different ways to compute singular values. The easiest is to compute the singular values without the singular vectors. Use svd with one output argument, s1.... read more >>

A few days ago, a bug report from our office in Cambridge caught my attention. Computing the singular values and singular vectors of a particular matrix would sometimes cause MATLAB to crash.... read more >>

(I have a guest blogger today. Ron Jones worked with me in 1985 for his Ph. D. from the University of New Mexico. He retired recently after nearly 40 years at Sandia National Labs in Albuquerque and now has a chance to return to the problem he studied in his thesis. -- CBM)... read more >>

This blog post describes Qube, my Rubik's Cube simulator. Source code for Qube is now available in one single file from this link: Qube_osf.m. I will also submit the code to the MATLAB Central File Exchange. As usual, I welcome any feedback.... read more >>

This is about linear systems with fewer equations than variables; A*x = b where the m -by- n matrix A has fewer rows that columns, so m < n . I have always called such systems wide or fat, but this is not respectful. So I consulted the Merriam-Webster Thesaurus and found commodious.... read more >>

The rank of a linear transformation is a fundamental concept in linear algebra and matrix factorizations are fundamental concepts in numerical linear algebra. Gil Strang's 2020 Vision of Linear Algebra seeks to introduce these notions early in an introductory linear algebra course.... read more >>

I have added this section to my post a few weeks ago about using the SVD to measure partisanship in the United States Senate.... read more >>

Many observers have noted that the United States Senate has become increasingly partisan in recent years. Votes are being made more frequently along strict political party lines. The singular value decomposition, the SVD, of matrices derived from records of roll call votes in the senate can measure this partisanship.... read more >>

Tomorrow, February 29, 2020 would be Gene Golub's 22nd birthday.... read more >>