# Season’s Greetings Fractal6

Posted by Cleve Moler,

I don't recall where I found this seasonal fractal. And I can't explain how it works. So please submit a comment if you can shed any light on either of these questions.... read more >>

# My First Matrix, RGB, YIQ, and Color Cubes2

Posted by Cleve Moler,

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.... read more >>

# Four Fundamental Subspaces of Linear Algebra, Corrected

Posted by Cleve Moler,

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

# Four Fundamental Subspaces of Linear Algebra3

Posted by Cleve Moler,

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

# My Favorite ODE

Posted by Cleve Moler,

My favorite ordinary differential equation provides a good test of ODE solvers, both numeric and symbolic. It also provides a nice illustration of the underlying existence theory and error analysis.... read more >>

# Apologies to Gram-Schmidt

Posted by Cleve Moler,

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 >>

# Compare Gram-Schmidt and Householder Orthogonalization Algorithms4

Posted by Cleve Moler,

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 >>

# Householder Reflections and the QR Decomposition1

Posted by Cleve Moler,

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.... read more >>

# Matrix Multiplication Flexes House

Posted by Cleve Moler,

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