I have spent much of my career working to bring abstract linear algebra and practical matrix computation closer together. This project is my latest effort.... read more >>

I have just returned from a one-day workshop at U. C. Santa Barbara honoring John Gilbert on his 70th birthday and his official retirement after 20 years on the UCSB faculty.... read more >>

While it is still fresh in my mind, I want to describe the conversation I had with a publicly available version of ChatGPT, the much-discussed large language model, LLM, for conversational artificial intelligence.... read more >>

Christian Reinsch and Roland Bulirsch both passed away recently, Reinsch on October 8 and Bulirsch on September 21. Reinsch was 88 years old and Bulirsch was 89. Both of them were retired professors of numerical analysis at the Technical University of Munich. Both of them were friends of mine. But in almost all other ways, they were very different people.... read more >>

The Soma Cube brings back memories.... read more >>

Rubik's Cube is one of the great mathematical puzzles of all time. Most people are just interested in solving Rubik's Cube rapidly, but deeper investigation reveals a rich mathematical and computational structure. A digital Rubik's Cube simulator provides a laboratory for the study of linear algebra, group theory, data structures and computer graphics.... read more >>

My recent obsession with cubes in this blog has led me back to Rubik's cube, perhaps the greatest mathematical puzzle of all time.... read more >>

On a recent visit to Ann Arbor, I met ten-year old Eden Rajapakse. Here is her sketch of the L-shaped membrane. Download Live... read more >>

The Menger sponge is a popular fractal that generalizes Cantor sets and Sierpinski triangles. Its fractal dimension is between two and three.... read more >>

Quaternions are generalizations of the complex numbers that have found applications in computer graphics and many other fields.... read more >>