Question

Hey guys, I am learning linear algebra frim OCW and it is really helpful. but the thing that occupies my mind anytime I study this course is that why we use matrices in the first place? What is their actual meaning?

Answer 1

well according to my math major checklist sheet Linear Algebra is under computer science.

Answer 2

What is OCW? I have to review some linear algebra myself...been too long since I took it.

Answer 3

leaving comment for answer (also taking up linear algebra, philippines)

Answer 4

I meant mit open course ware

Answer 5

Matrices are very useful though, especially when dealing with vectors and space...makes everything easier I think @ganeshie8 can explain it better as it's been too long for me.

Ooh that sounds great, could you link it if you don't mind?

Answer 6

@Empty

Answer 7

I was going to tag @Empty but I thought he was too busy xD

Answer 8

I think its kinda related to systems of linear equations.

Answer 9

I've heard of mit open course ware... I think dan recommended it to me for pdes or something I can't remember

Answer 10

http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/lecture-1-the-geometry-of-linear-equations/

Answer 11

Matrices represent not just systems of equations and vectors. They can represent any sort of geometric manipulation you could want such as rotations, translations, shearing, scaling, and weird stuff, and you can multiply all the translations together to create a single translation which you can then apply onto anything, which ends up being really useful for doing all 3D computer graphics and modelling physics scenarios. You can also use them to create interpolating functions for data, so they are useful especially for interpreting data with a computer.

In my mind calculus and linear algebra are the two most important things in mathematics, and the more you learn, the more these two end up becoming the same subject.

I have a lot of examples I could show you, but this is basically just an overview. They really only started becoming used in the past 100 years when Heisenberg formulated quantum mechanics with them.

Answer 12

Well said, awesome and inspiring as always!

Answer 13

Yes was really helpful

Answer 14

@hamid.rajabi I can answer any questions you have if you want some more specific examples on certain things. :)

Answer 15

How does calculus and linear algebra relate to each other? Like cross products kind of stuff, jacobians?

Answer 16

:-) thanks alot. These matrices really got something in them. and I have seen them inso many engineering applications

Answer 17

a matrix represents some linear function between vector spaces

Answer 18

Yeah, I am specifically thinking of Jacobians, vector calculus, and tensor calculus.

Answer 19

In mit lectures professor strang says that we use 'too much calculus'. He is kinda against excessive use of calculus

Answer 20

Ah got ya, I've always wanted to see linear algebra in physics problems like I know you can use it for hooke's law, kirchhoff's law, etc. I actually have this one space probe problem in mind I'd like to see, would you mind if I post it here @hamid.rajabi

Answer 21

I really love Strang's OCW stuff I still go back to it sometimes to review but I think it's best if you really use linear algebra AND calculus, they both work well together. For instance, quadratic form minimization really is something that's a strength of combining both things together.

Answer 22

Its ok @astrophysics

Answer 23

Haha, well I think I'm going to try figuring out the problem first, and if I have problems with it I'll just make a post, thanks for the post though :)

Answer 24

Matrices help order stuff, without them some things may look very clustered
For example to find the area of a triangle when it's coordinates are given you use a very long and hard to remember formula, but if you represent it as a determinant it is much easier to remember, also determinant can also be used to represent cross product of 2 vectors in a much more neat way

Answer 25

Good old Gilbert Strang... I watched those videos too when i took that class, helped out a bunch.

Answer 26

@DanJS yeah man he's great. where did you study? Mit?