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 want to share some colorful images featuring the seven colors in the MATLAB axes color order.... 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 >>

Line plots with a color order from one of our color maps are useful, and pretty.... read more >>

The floating point arithmetic format that occupies 128 bits of storage is known as binary128 or quadruple precision. This blog post describes an implementation of quadruple precision programmed entirely in the MATLAB language.... read more >>

This is a follow-up to my previous follow-up, posted several days ago. A very careful reader, Bruno Bazzano, contributed a comment pointing out what he called "a small typo" in my code for the classic Gram-Schmidt algorithm. It is more than a small typo, it is a serious blunder. I must correct the code, then do more careful experiments and reword my conclusions.... read more >>

This is a follow-up to my previous post. Classical Gram-Schmidt and Modified Gram-Schmidt are two algorithms for orthogonalizing a set of vectors. Householder elementary reflectors can be used for the same task. The three algorithms have very different roundoff error properties.... read more >>

Magic Stars are a little like Magic Squares. My grandson was introduced to them in his junior high school math class.... read more >>

I have just returned from the huge Supercomputing 2012 conference in Salt Lake City. I can report on interesting reactions to some questions I posed in last week's blog and on some impressive speedup results when we ran the code in last week's blog on a parallel cluster in the Cloud.... read more >>