In what ways are matrices used in the real world?
In: Mathematics
Matrices is used to describe linear function (or relatedly, affine function), and metric tensor, all of which come from linear algebra. Linear algebra is a very useful topic that seep into pretty much everything, because it’s one of the most well-understood math topic. Think about it. Even if you know that your car don’t move at constant speed, you still think of its speed as an useful. Even though we know that trend don’t keep moving, we still try to predict where it will go if it keeps going. Even though we know light don’t go straight, we still treat it as straight line. We understood linear stuff well, and we try to reduce more complicated things to it as our first approximation. Which is why linear algebra is everywhere.
Just 2 examples:
– Statistics: principal component analysis and linear regression are 2 common tool in statistics. They allow you to see how one data can linearly varies with another. Since statistics get applied everywhere, linear algebra has a lot of application.
– Physics: very generally, physics study symmetries of the world. How do they represent symmetries? Through group of linear functions. At the most basic level, everyday life geometry can be represented this way, your symmetries are translation and rotation (this has application in gaming, robotic, aviation, etc.). At the more advanced level, you have gauge theory. And that’s not to mention other application in physics that’s hard to explain in ELI5.
The above didn’t even include matrix not being used in the context of linear algebra, which is just an array of number.
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