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.... 続きを読む >>
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.... 続きを読む >>
Computing Eigenvalues of Symmetric MatricesSee revision.Get the MATLAB code (requires JavaScript) Published with MATLAB®... 続きを読む >>
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.... 続きを読む >>
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.... 続きを読む >>
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.... 続きを読む >>
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.... 続きを読む >>
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.... 続きを読む >>
Recently, I had email from a student in Italy.... 続きを読む >>
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.... 続きを読む >>
