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> If you are familiar with linear algebra Could you please write what are some common day to day life applications of linear algebra in computing?

• wongarsu 3y ago
  The obvious fields are computer graphics (all kinds: 2d, 3d rasterized and 3d raytraced are all heavy on linear algebra, though 3d rasterized is the easiest to speed up with the lockstep SIMD architectures we call GPUs) and neural networks. Computer graphics mostly because you can view the real world as 3d space and the screen as 2d space, and linear algebra gives you all the tools to manipulate something in 3d space and project it into 2d space. Neural networks because you can treat them as matrix multiplications.
• juujian 3y ago
  I have really lost touch with common day to day life at this point, but Excel would be an excellent example. If you have a column with a million data points and do some basic calculation -- subtract or multiply another column -- whether or not the software you use can translate that into a vectorized operation under the hood using linear algebra can significantly speed up your operation.
• dreamcompiler 3y ago
  Nvidia exists because linear algebra is essential for 3D graphics. They got a second boost from crypto-currency, which isn't strictly about linear algebra but it can put those computation units to good use. Now Nvidia is riding high again because neural nets are all about linear algebra, and LLMs are big neural nets.
  • visarga 3y ago
    I would also add scientific simulations to the list of tasks that GPUs are used for. They parallelise well on many cores.
• JamesLeonis 3y ago
  Linear Algebra is like a lot of math in CS; you don't necessarily see it initially, but once you get some familiarity you start seeing it everywhere. Others have commented on computer graphics, but (as it turns out) the exact same algorithms apply for Collision Detection in 3D space. And since games already are manipulating graphics, you add on another set of Linear Algebra transforms that change the position/rotation/shear of those vertices. In a similar way, science (especially physics) use linear algebra to build simulations of all kinds of systems. One surprising use is in Advertising (and other user preference aggregators). Turns out a preference acts like a magnitude of a one-dimensional vector. String N preference vectors together and you get an N-Dimension Vector that you can perform Linear Algebra operations upon. One common application is the Dot Product, which is a fancy way of taking two N-Dimension vectors and measuring how close those vectors point in the same direction in a [1, -1] range. Yet another common place to find Linear Algebra is in computer science papers. Most of the time this is simply notation; a lot of common programming forms can be represented by MxN matrices. However some of those algorithms will use LA as a way of parsing and breaking down a problem. You will see this in compiler papers often, but its transferable to many other domains. As a final and personal observation, I found that Linear Algebra helped me grasp Functional Programming. In both cases I am applying a transform to some input, and often stringing together many such transforms. Also in both cases, the transformations are sensitive to their order, and a bad ordering produces nonsense just like garbage data.
  • visarga 3y ago
    > One common application is the Dot Product , which is a fancy way of taking two N Dimension vectors and measuring how close those vectors point in the same direction in a [1, 1] range. That's cosine similarity, or normalised dot product. The dot product can take any value when the vectors are not unit norm.