What are cool applications of it?
My linear algebra class pretty much only focused on theory and proving stuff, with only the odd practical example.
>>7712162
Mostly all physical sciences/math. But there are an odd-ball or two applications to social sciences/marketing (mostly simple linear regression though). Quantum Mechanics is a biggie.
>>7712162
Sparse matrices are useful in natural language processing. SVD is used for dimensionality reduction and you can do all sorts of calculations with the row vectors of a WORDSxDOCUMENTS matrix
>>7712162
Data Mining uses it extensively. So does anything involving graphics. Your computer's GPU? It's a linear algebra machine. Data Science in general uses linear algebra a lot.
I hear engineering (real engineering, not "put engineering at the end of every adjective" memery) uses it a lot but I'm not in that field so I don't know.
>>7712162
In 3 years, you'll be wonder why the fuck didn't you learn it in middle school.
>>7712162
Optimization is a nice one, and about as applied as you can get without going to shit. Check out Luenberger's book.
>>7712179
>Quantum Mechanics
This. If we're being pedantic, QM is actually an application of functional analysis (the linear spaces aren't finite-dimensional ones LA studies at length) but you can pretend the same proofs work and won't run into too much trouble for the most part.
I think computer graphics too, but I have no clue what that field entails or whether it's highly theoretical/nontrivial or more like baby's first matrix manipulation. I do know the Jordan canonical form makes numerical computation easier, and a good constructive proof lends itself to computing.
>>7712363
AFAIK the interesting math in computer graphics isn't the linear algebra, which is very basic
>>7712162
Transformations are pretty important important. Applications in relativity. (Relating a euclidean reference frame to an accelerated reference frame involves the use of the Lorentz transformation, which is basically just a linear transformation that maps R4 onto R4)
Also transformation equations are how your computer knows what pixels to light up on your screen. So basically any computing that involves some sort of user interface uses linear algebra
computational physical chemistry is almost entirely linear algebra. You can break down quantum mechanical descriptions of molecular systems into a metric fuckload of linear equations of many variables and run it through a computer.
>>7712205
Yes it does pretty much all engineers solve problems involving simultaneous linear equations. The field of statics is basically just applied LA. EEs do a lot with nodes which are basically optimization problems
>>7712379
To add to this in ChemE a lot of material and heat balances are solved using linear systems. Linear algebra carries into transport phenomena pretty well.
Linear algebra is pretty much advanced engineering mathematics. Finite element, transformation, mapping and so on. We are talking real engineering ... Civil, mech, petroleum and so on. My knowledge is bit weak in physical science but Im sure it would be used a lot as well.
