| I write a blog on math and programming and I see linear algebra applied every day. 1. Ranking in search engines (more generally, any kind of random walk analysis) [1] 2. Fourier analysis, and as a consequence most signal processing involves some understanding of linear algebra because integrals are linear. [2] 3. Regression [3] and more generally linear modeling of anything. 4. Facial recognition [4] 5. Community detection [5], where most leading methods analyze the spectrum of a graph to find communities. In fact, applied network science in general has a ton of linear algebra. 6. Greedy algorithms are characterized by a kind of generalization of linear systems [6] 7. Linear programming, perhaps the most applied piece of mathematics ever, needs a strong foundation of linear algebra [7] 8. All of quantum computing is literally just linear algebra [8]. 9. Cryptography has a ton of linear algebra in it, and a large portion of the techniques are reasoned about with linear algebra. 10. Most of calculus relies on linear algebra, most importantly optimization [9] 11. Recent data analysis techniques based on topology do so through linear algebra [10] 12. Coding theory, including the algorithms used to correct errors on DVDs. Basically, any time you want to encode data so that you can recover from white noise, you're going to use a linear code. [11] This includes compression techniques. 13. Of course graphics. I could go on... [1]: http://jeremykun.com/2011/06/12/googles-pagerank-introductio... [2]: http://jeremykun.com/2012/07/18/the-fast-fourier-transform/ [3]: http://jeremykun.com/2013/08/18/linear-regression/ [4]: http://jeremykun.com/2011/07/27/eigenfaces/ [5]: http://jeremykun.com/2014/05/19/community-detection-in-graph... [6]: http://jeremykun.com/2014/08/26/when-greedy-algorithms-are-p... [7]: http://jeremykun.com/2014/06/02/linear-programming-and-the-m... [8]: http://jeremykun.com/2014/12/08/a-motivation-for-quantum-com... [9]: http://jeremykun.com/2013/11/30/lagrangians-for-the-amnesiac... [10]: http://jeremykun.com/2013/04/10/computing-homology/ [11]: http://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_corr... |