Results for: Matrices

Wilkinson’s Matrices

Posted by Cleve Moler,

One of Jim Wilkinson's outstanding skills was his ability to pick great examples. A previous post featured his signature polynomial. This post features his signature matrices.... read more >>

Hilbert Matrices 6

Posted by Cleve Moler,

The inverse Hilbert matrix, invhilb, has recently made surprise appearances in Cody, the programming game on MATLAB Central, and one of Ned's posts in the MATLAB Spoken Here blog. Inverse Hilbert matrices had nearly been forgotten in MATLAB. Their comeback is due to the sign pattern of their entries. But I want to take you back to their original role demonstrating ill conditioning in numerical calculation.... read more >>

Game of Life, Part 1, The Rule 1

Posted by Cleve Moler,

This is part one of a series of posts about John Conway's Game of Life. One deceptively simple rule leads to an incredible variety of patterns, puzzles, and unsolved mathematical problems, and a beautiful use of MATLAB sparse matrices. ... read more >>

Symmetric Pair Decomposition 1

Posted by Cleve Moler,

An esoteric fact about matrices is that any real matrix can be written as the product of two symmetric matrices. I've known about this fact for years, but never seriously explored the computational aspects. So I'm using this post to clarify my own understanding of what I'll call the symmetric pair decomposition. It turns out that there are open questions. I don't think we know how to reliably compute the factors. But I also have to admit that, even if we could compute them, I don't know of any practical use.... read more >>

Symplectic Spacewar 4

Posted by Cleve Moler,

This is the probably the first article ever written with the title "Symplectic Spacewar". If I Google that title today, including the double quotes to keep the two words together, I do not get any hits. But as soon as Google notices this post, I should be able to see at least one hit. ... read more >>