Singular Value Decomposition

That's quite the hyperbole.

When I was studying Electrical Engineering, I noticed that SVDs cropped up frequently. From memory, a quick list of situations where I can recall using SVDs :

- For computing homographies in Computer Vision

- For clustering in Machine Learning

- For noise reduction in DSP

In general, when the problem can be modeled using linear algebra, SVD often proves to be a versatile tool ( for linear optimization, eigenvalue problems, least squares, etc).

However, that doesn't make it the most important topic. I could just as easily name a bunch of other techniques that are also frequently used : FFTs, Linear programming, Monte Carlo methods. If you're an electrical engineer, all of these would be useful. Yet, I wouldn't call any of them the most important topic.

In response to ha-hn:

The intent to this post is not to create mathematical elitism, but to highlight an important mathematical concept that comes up in programming--and many programmers may work with or around it without realizing it.

As I understand it, this concept is used in: * Compression Algorithms * Signal Analysis * Pagerank * Factor Analysis * Animation (especially when considering more than 3 points of information for each vector) * Clustering in Machine Learning * Noise reduction in DSP * Match.com's dating algorithm * Principal Component analysis * Image scaling * Control theory

I know it has been used in many more applications beyond this list.

I'm sorry you feel a smack of mathematical elitism. The concepts here are not inherently difficult, just a little complex. Here is a great resource to learn more: http://www.puffinwarellc.com/index.php/news-and-articles/art...

Sure, but also it's better to look for the common case (i.e. the 80%) and make sure that's fast. It's not always worth optimizing the uncommon case (like branch misses with a branch predictor).