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

# Four Fundamental Subspaces of Linear Algebra, Corrected

Posted by **Cleve Moler**,

**Category:**- Matrices,
- People,
- Singular Values

Blogs

Posted by **Cleve Moler**,

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

**Category:**- Matrices,
- People,
- Singular Values

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 >>

**Category:**- Matrices,
- People,
- Singular Values

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 >>

Posted by **Cleve Moler**,

I am launching a project that I call *Cleve's Laboratory*. My most recent Cleve's Corner column in MathWorks News & Notes is about the project. The MATLAB app itself is available for download from the MATLAB Central File Exchange.... read more >>

**Category:**- Fun,
- History,
- Logo,
- Numerical Analysis

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 >>

**Category:**- Algorithms,
- Magic Squares,
- Matrices,
- Numerical Analysis

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 >>

**Category:**- Algorithms,
- Magic Squares,
- Matrices,
- Numerical Analysis

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 >>

**Category:**- Algorithms,
- History,
- Matrices,
- People

Posted by **Cleve Moler**,

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

Posted by **Cleve Moler**,

MATLAB Central is celebrating its 15th birthday this fall. In honor of the occasion, MathWorks bloggers are reminiscing about their first involvement with the Web site. My first contribution to the File Exchange was not MATLAB software, but rather a collection of documents that I called the Pentium Papers. I saved this material in November and December of 1994 when I was deeply involved in the Intel Pentium Floating Point Division Affair.... read more >>

Posted by **Cleve Moler**,

Jim Sanderson has had a fascinating professional life. He was my PhD student in math at the University of New Mexico in the 1970s. He spent almost 20 years as a computational scientist at Los Alamos National Laboratory, working on the lab's supercomputers. He then developed an interest in ecology, went back to school, and is now the world's leading authority on the preservation of small wild cats around the world.... read more >>

**Category:**- conservation,
- History,
- Numerical Analysis,
- People

*These postings are the author's and don't necessarily represent the opinions of MathWorks.*

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