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I keep hearing about "linear algebra" and although I'm a third year engineering student and am finished with all of my dedicated math courses, I've never taken a course with that title. Looking at this guys videos, it seems like it's just "matrices and vectors" which I've done over the years during high school and in my Calculus courses.

It that all it is, or am I misunderstanding. Everybody seems to think that this field of math is very important, I feel like I should know it by now.




It can be tempting to reduce linear algebra to 'matrices and vectors', but there is more to it. Often times you can find a 'matrix algebra' course or something along those lines (I remember taking 'computational matrix algebra'), which really does pretty much just discuss computations with matrices and vectors. Linear algebra has more to do with the properties of vector spaces and 'linear transformations' on vector spaces—which can be represented using matrices, but there are deeper underlying concepts than the matrix computations themselves.


It is a very practical field of math, especially for computer scientists (Graphics, some variants of machine learning, pretty much any large scale computation with chunks that can be processed in parallel), which is probably where people derive importance from. Another huge benefit is that linear algebra (For matrices with certain properties, not generally) often allow for iterative and approximate solutions, which can make linear algebra a more tractable computational route. Some of your engineering classes may have used numerical solvers that rely on linear algebra to iteratively obtain relatively precise solutions to difficult equations.

You are correct that the fundamentals (Vectorized computation, aka matrices) are often introduced early on. The level at which you interface with linear algebra often scales with the level of math you are at. You can add them [1], integrate them [2], and use them to solve some PDEs [3]. You can see how all these "levels" of linear algebra would be accompanied by another math class pushing you to utilize linear algebra at a higher level than before. It appears that you're at the first level. I've actually never done [2] in the classroom, but [3] was introduced to me in a class on differential equations that utilized matrices as a possible solution route.

If you are interested in learning more, Khan academy has good linear algebra videos.

[1] http://www.purplemath.com/modules/mtrxadd.htm [2] https://www.youtube.com/watch?v=z73ed-bd9ek [3] http://www.maths.manchester.ac.uk/our-research/research-grou...


There are many excellent courses available online if you wished to take a look.

See MIT OCW Scholar's Linear Algebra offering: https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algeb...

Take a look at the final exam and see if it seems like something you've seen. If not, I strongly urge you to consider studying the subject.

A book that shows linear algebra's applications at a more advanced level is Strang's Computational Science and Engineering: http://math.mit.edu/~gs/cse/


>, I've never taken a course with that title.

I don't know about UK curriculum but the colleges in USA like MIT/Stanford/Princeton/etc have courses focusing on linear algebra (matrix math). Example:

https://explorecourses.stanford.edu/search?view=catalog&filt...

One of those classes is often taken as an elective to meet one of the math requirements for graduation.




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