What is linear algebra?

For the discussion of math. Duh.

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jewish_scientist
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What is linear algebra?

Postby jewish_scientist » Thu Oct 05, 2017 12:11 pm UTC

Considering I studied lines and their equations in middle school and a prerequisite to my college's linear algebra class is Calculus I, I am going to go out on a limb here and guess that linear algebra is not what I think it is.

Demki
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Re: What is linear algebra?

Postby Demki » Thu Oct 05, 2017 12:44 pm UTC

Linear algebra is less about "lines and their equals" and more about vector spaces, and linear functions between them.
Linear functions are functions that preserve vector addition and multiplication by a scalar.
In linear algebra you'll learn what a vector space is, and you'll learn about matrices and operations on matrices, among other things.

Here are a few videos on linear algebra by 3blue1brown(Grant Sanderson), which explain some of the ideas behind linear algebra using appropriate visuals. They are not a replacement for actually learning linear algebra.

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Thesh
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Re: What is linear algebra?

Postby Thesh » Thu Oct 05, 2017 4:47 pm UTC

It is related, however. It pretty much all starts with learning to solve systems of linear equations using matrices, and expands from there. So while it quickly goes into vector spaces, it is really a continuation of the linear algebra you learned in middle school.
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Eebster the Great
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Re: What is linear algebra?

Postby Eebster the Great » Thu Oct 05, 2017 5:31 pm UTC

I failed to appreciate how complicated simple concepts can become until I learned how to prove that 1+1=2. (This isn't a remotely complicated proof in any system, as far as I know, but it is still substantially more complicated than I expected it to be.) Linear algebra at its very heart is sort of what you expect it to be, but its complexity might still surprise you.


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