Here's just a fraction of what the can do with linear algebra

Here's just a fraction of what the can do with linear algebra

The next time someone wonders what's the point of linear algebra are, send them here. I write a blog on math and programming and I see linear algebra applied to computer science all the time. Here's a short list this comprises a small fraction of the things you can does with linear algebra.

Ranking in search engines: The most high-profile use of linear algebra (whether or not you know it) is in the creation of Google. Their original ranking algorithm, which have since surely become far more complicated, used a lot of linear algebra to rank Which webpages should show up first. More generally, any time want to analyze a random walk in a network, you ' re likely to need some linear algebra. Here's a series of blogs posts I wrote deriving the method.

linear programming: the Most widely used application of linear algebra are definitely optimization, and the most widely used kind of optimization I s linear programming. You can optimize budgets, your diet, and your route to work using linear programming, and this only scratches the surface of the applications. Here's a series (still in progress) on the mathematics behind linear programming. The primary technique for solving them, called the simplex algorithm, was essentially a beefed up Gaussian elimination.

error Correcting codes: Another unseen but widespread use of linear algebra are in coding theory. The problem is to encode data in such a by the if the encoded data is tampered with a little bit, can still recover The unencoded data. Such schemes is called error correcting codes, and the simplest ones encode data as vectors in a vector space. Error correcting codes is used in DVDs to prevent scratches from ruining a movie. They ' re also used on deep space probes to transmit data back to Earth, and they allowed us to get the first ever close-up Pictures of Saturn and Jupiter. Here's an article describing the simplest kind of error correcting code, the Hamming code.

signal Analysis: the field of signal analysis gives one massively useful tools for encoding, analyzing, and manipulating "signals" so can be audio, Images, video, or things like X-rays and light refracting through a crystal. The simplest-understand the Fourier transform is as a linear map, performs a change of basis. Fourier analysis had even been used to make art. Here's the first post in a series deriving Fourier analysis from scratch, although much of it can be abbreviated, skipped, Or skimmed if you have a strong understanding of linear algebra. A discrete cousin of Fourier analysis have been part of many theoretical techniques in computer science as well.

graphics: Pretty much all The graphics innovation since computers have existed with come from video games and movies. The central part of the graphics are projecting a three-dimensional scene onto a two-dimensional screen. Projection is already a linear map. On top of that, rotations, scaling, and perspective is all implemented and analyzed properly using linear algebra.

facial recognition: A Cool (but not the most) method for doing automated facial recognition uses a linear algebraic technique called princ Ipal component analysis. Essentially this was just finding a particularly good basis to represent a database of the face images, and using eigenvectors ("Eigenfaces") to rebuild the images. Here's an article describing the without prior knowledge of PCA, and a more general article showing PCA for any D Ataset. Here's a picture of the "eigenface" might look like.

Prediction: The simplest models of prediction is linear models, and these is developed and understood with linear algebra. Here, for example are an article describing how to do linear regression.

Community Detection: The leading methods for detecting communities in networks of people (or any other kind of network) use a Linear-algebraic Tool called the spectrum of the network. Like ranking webpages, community detection techniques also rely on random walks. Here are an overview of some notions of community detection.

Greedy algorithms: Greedy algorithms is characterized by a kind of generalization of linear systems called a matroid. In other words, every problem solvable by a greedy algorithm can is represented as a matroid and every matroid can be Opti Mized by a greedy algorithm. Understanding linear algebra is not a requirement to understand matroids, but it makes the process much easier. Here is a article proving what I just said.

Quantum Computing: All of quantum computing are literally just linear algebra, as are general quantum mechanics. Can understand how quantum computers can break cryptosystems without any physics, as long as you understand linear ALG Ebra. Here are the first of a series of articles (in progress) doing this, and it gives you a idea of how linear algebra is the Primary tool.

There is vastly more applications of linear algebra than I can list here, from cryptography to data analysis to medical I Maging and beyond. But the point was Clear:a Strong foundation in linear algebra was all kinds of useful.

Here's just a fraction of what the can do with linear algebra