Matrices like the ones shown in the following screen shots are at the heart of computer graphics. They describe objects moving in three-dimensional space. MATLAB's Handle Graphics uses them. So does MathWork's new RoadRunner editor. And so do all popular video games and CAD packages.... read more >>
I am giving a five-minute talk today, May 26, at the virtual seminar on Complexity of Matrix Computations. Here are my slides. Two new MATLAB functions, tred and imtql, instrumented to count flops, are available in symeig.m.... read more >>
Computing Eigenvalues of Symmetric MatricesSee revision.Get the MATLAB code (requires JavaScript) Published with MATLAB®... 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 >>
What do Mount St. Helens and the rank of a matrix have in common? The answer is the MATLAB function peaks. Let me explain. Please bear with me -- it's a long story.... 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 >>
My post a few days ago, Gil Strang and the CR Matrix Factorization, generated a lot of email. Here is the resulting follow-up to that post.... read more >>
My friend Gil Strang is known for his lectures from MIT course 18.06, Linear Algebra, which are available on MIT OpenCourseWare. He is now describing a new approach to the subject with a series of videos, A 2020 Vision of Linear Algebra. This vision is featured in a new book, Linear Algebra for Everyone.... read more >>
Recently, I had email from a student in Italy.... read more >>
While I was working on my posts about Pejorative Manifolds, I was pleased to discover the intriguing patterns created by the roundoff error in the computed eigenvalues of triple Kronecker products.... read more >>
