
Ask HN: Should I learn Linear Algebra? Why? - lokiju
Broad question by design, I think it would be cool and helpful to see what reasons people have to learn linear algebra.
======
jlangemeier
Computer Graphics; Data Science; and ML/AI are your obvious ones. Most
engineers can benefit from it, because all you're doing is modelling systems;
take a look at how Spice programs model electrical circuits as an example of
this. There's a lot of math that needs an understanding of vector spaces to
grasp the concepts. Most Lin Alg books and courses that are more geared
towards graduate level students (so folks with the basic lin alg info under
their belt) work on generalization, and it directly leads to some interesting
applications in probability, graph theory, number theory, and a whole host of
other more advanced topics. There's even whole programs built around solving
things from a linear algebra perspective (see MatLab for example)

Linear algebra is just a tool that fits nicely in a lot of computer science
and various engineering toolboxes.

------
kingkongjaffa
For the everyday developer messing with data, there are some nice concepts to
know.

I'm talking super basic like when is it useful to transpose a dataset, to
apply some function, then transpose back?

Being congnizant of the data-shape is something that comes as a side effect of
studying linalg and matrices.

Just recognizing things like that will be the most value add unless you get
into some domain specific requirements (games/engineering software).

------
impendia
Here's a fun problem which can be solved by linear algebra.

You have a group of 20 people. Each of them rates how much they like everyone
else, on a scale of 1 to 10. Your task is to figure out how popular everyone
is, again on a scale from 1 to 10. Someone's "popularity" is based on how much
the other kids like them, except the cool kids' opinion count more. You're
popular if the popular people like you.

Can you mathematically compute how popular everyone is? Is the solution
unique? Or might there be more than one solution? The problem seems hopelessly
circular -- you have to figure out who is popular before you can figure out
who is popular -- but actually it turns out to be a standard linear algebra
problem.

~~~
tcbasche
Ooh that's cool - can you elaborate on the solution?

~~~
impendia
Suppose that the popularities of everyone are p_1, p_2, through p_20. Then, if
you write "~" for "is proportional to", you get a bunch of equations like

0p_1 + 8p_2 + 4p_3 + ... + 4p_20 ~ p_1

7p_2 + 0p_2 + 7p_3 + ... + 9p_20 ~ p_2

...

if you assume that Person #1 is rated 8 by Person #2, 4 by Person #3, and so
on, and that nobody rates themselves.

Anyway, you can combine these into a matrix equation

Mv = cv

where M is the matrix with all the popularity ratings that students give each
other, v is a vector which says how popular everyone is, and c is a constant.
M is known, and you have to solve it for v and c.

Anyway, v is an _eigenvector_ of the matrix M, and finding them is a standard
problem.

[https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors](https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors)

The same idea shows up all over the place in linear algebra.

~~~
BOOSTERHIDROGEN
I still can't grasp the concept of eigenvalues and eigenvectors, any
references that have good and intuitive explanations, thanks

~~~
stadeschuldt
The videos of 3blue1brown are very good:

[https://www.youtube.com/watch?v=PFDu9oVAE-g](https://www.youtube.com/watch?v=PFDu9oVAE-g)

------
cinntaile
If you want to do ML/AI or scientific computing then it's a pretty useful
skill to have.

