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The Menger Sponge Fractal 1

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

Quaternions 3

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

Computers That I Have Known

Nick Higham's Numerical Linear Algebra group at the University of Manchester is hosting a conference celebrating Jack Dongarra's 70th birthday July 7 and 8. I am giving a talk, virtually, on July 7. I plan to reminisce about how I did computing in the days before everybody had their own computer in their lap. Here are the slides for the talk, some notes, and some links to this blog for more details.... 更多内容 >>

A Famous Equation, x^2 = 2^x

A recent episode of the popular YouTube channel "blackpenredpen" is about solutions to the famous equation... 更多内容 >>

Notes on CR and west0479 4

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.... 更多内容 >>

Gil Strang and the CR Matrix Factorization 4

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.... 更多内容 >>

SVD Quantifies Increasing Partisanship in the U. S. Senate 5

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.... 更多内容 >>

Collatz Inequality and Singleton Expansion 2

I've blogged about this gem from Lothar Collatz (1910-1990) before, but it deserves to be repeated. Especially since it now provides an elegant example of singleton expansion.... 更多内容 >>

Serendipity, Kuramoto, Colleagues and Backslash

Alexa tells me that the definition of serendipity is "the occurrence and development of events by chance in a happy or beneficial way."... 更多内容 >>

Posts 11 - 20 of 90