The adjacency matrix of a hypercube demonstrates the new MATLAB graph object.... 더 읽어보기 >>

When I was in high school in the 1950's, I didn't know anything about matrices. But I nearly encountered one when I wrote a paper for my physics class about the color scheme that allowed new color TV broadcasts to be compatible with existing black-and-white TV receivers.... 더 읽어보기 >>

(Please replace the erroneous posting from yesterday, Nov. 28, with this corrected version.)... 더 읽어보기 >>

Here is a very short course in Linear Algebra. The Singular Value Decomposition provides a natural basis for Gil Strang's Four Fundamental Subspaces.... 더 읽어보기 >>

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.... 더 읽어보기 >>

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.... 더 읽어보기 >>

The QR decomposition is often the first step in algorithms for solving many different matrix problems, including linear systems, eigenvalues, and singular values. Householder reflections are the preferred tool for computing the QR decomposition.... 더 읽어보기 >>

A new app employs transformations of a graphic depicting a house to demonstrate matrix multiplication.... 더 읽어보기 >>

A few days ago we received email from Mike Hennessey, a mechanical engineering professor at the University of St. Thomas in St. Paul, Minnesota. He has been reading my book “Numerical Computing with MATLAB” very carefully. Chapter 7 is about “Eigenvalues and Singular Values” and section 10.3 is about one of my all-time favorite MATLAB demos, eigshow. Mike discovered an error in my description of the svd option of eigshow that has gone unnoticed in the over ten years that the book has been available from both the MathWorks web site and SIAM…. 더 읽어보기 >>

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…. 더 읽어보기 >>