linear algebra is one of the most useful fields of mathamatics their is. It is used in almost all engineering disciplenes . Especially Mechanical Engineer, Aerospace Engineering and Computer Science
I had to take LA for my MIS degree
For some reason, I am good at the abstract theory stuff in both geometry and LA. The class was pretty fun from an intellectual standpoint, though for my profession I will never use it. My prof said about the only people who use it a lot are EE's.
I suspect it depends what level you are working at, and in what field. Even if you aren't using it explicitly, likely the tools you use do. And understanding how your tools do what they do is always critical.
For the stuff I work with most of the time, there aren't pre-packaged tools available. So I'm always down in the weeds, and when you're down in the weeds you never have enough math. As much math as I had in college (a minors worth, and more in grad school), I wish I had more!
Another CS example ... I'm getting out of my league here, but IIRC, all programs can be described using graph theory, and graph theory is all matrices.
are you joking or are you being serious? try writing any sort of 3d rendering program without understanding linear algebra... my point is, many programs don't use calculus (heck, most don't use trig or geometry or sometimes even algebra!!), but that doesn't mean that you won't need these tools at some point.
If you're in a good program, you can't get away from learning it.
physics classes will definately take advantage of linear algebra. especially when you hit quantum.
for the most part, the normal physics sequence engineers take isn't too bad -- nice, idealized problems that you can study and you're pretty confident that they'll show up on the exam. how i miss that
...now i just show up to exams hoping i can solve problems...argh...
I'm taking the highest level undergraduate quantum optics class at my university. We don't use linear algebra at all. It's all just multi-dimensional calculus / boundary value problems.
-Ankur
PS. Might I add that the class is BRUTAL.
-Ankur
PS. Might I add that the class is BRUTAL.
How do you NOT use linear algebra in a quantum course
<-- taking a quantum course right now. it's filled with the stuff
I've found Linear Algebra to be very easy so far (4th week of classes) you kinda have to step back from calculus to get a good grasp of it.
but what about subspaces and theory that goes with linear algebra?
I can see how eigenvalues, and general matrix computations are useful; but I fail to see how subspaces and the proofs that encapsulate vector spaces and such are useful.
I don't think you need to know what defines a subspace for those things.
But, you also don't need to know a lot of the theory behind calculus (or anything for that matter) to apply it. But being able to learn these things shows people that in "the real world" you will be able to master other complicated ideas.
alkemyst
No Lifer
- Feb 13, 2001
- 83,769
- 19
- 81
I think calc 2 and one higher level math is. I took Matrix Theory for that which uses a linear algebra book.
It's an interesting math for solving multiple formula problems.
You basically take all the coefficients, order them in column and get each 'column' to reduce to 1 at one row.
Å
It depends on your job. That's pretty fundamental stuff if you work in any problem-solving area, any academic setting, numerical modeling, etc. If you are on sales, or any less technical side of engineering, you will probably never use it, and the work will be given to someone else.
Gibson486
Lifer
- Aug 9, 2000
- 18,378
- 2
- 0
Who ever said engineers dont use Linear Algebra is smoking something or just is not paying attention. In EE, you use it in Circuits (kramers rule to solve for many linear equations). If you are an engineer and dont know the difference between R spaces, you are screwed.
I graduated in CE in 2002. Linear Algebra was required at my school up until my last year. They dropped it from the curriculum, and I didn't take it. It may come in handy for advanced water modeling or structural analysis, but I have yet to find a use for it.
Can someone give me a better idea what is exactly involved in this "solving system of equations" and "creating a matrix."
Are you talking about when you have 3 equations with 3 variables you need to solve for? Because I had that in sophomore year of HS so I hope that isn't what you're talking about
Are you talking about when you have 3 equations with 3 variables you need to solve for? Because I had that in sophomore year of HS so I hope that isn't what you're talking about
Here's the low down:
- You can definitely use linear algebra to solve sytems with n equations and unknowns. For example, you can do this for circuit analysis using your mesh analysis.
- If you are a computer science person, you will learn that you can use linear algebra for different sorts of algorithms. You can use them for your Cholesky decomposition, QR factorization, HouseHodder factorization, Gram-Schmidt process, etc.. HouseHodder is especially useful for reflection or rotating vectors without changing its magnitude. Can you say 3D programming?
- There are other useful things that I do not know about, yet.
Trust me. It will come haunt you back later.
- You can definitely use linear algebra to solve sytems with n equations and unknowns. For example, you can do this for circuit analysis using your mesh analysis.
- If you are a computer science person, you will learn that you can use linear algebra for different sorts of algorithms. You can use them for your Cholesky decomposition, QR factorization, HouseHodder factorization, Gram-Schmidt process, etc.. HouseHodder is especially useful for reflection or rotating vectors without changing its magnitude. Can you say 3D programming?
- There are other useful things that I do not know about, yet.
Trust me. It will come haunt you back later.
Originally posted by: Kev
Can someone give me a better idea what is exactly involved in this "solving system of equations" and "creating a matrix."
Are you talking about when you have 3 equations with 3 variables you need to solve for? Because I had that in sophomore year of HS so I hope that isn't what you're talking about
Let's say you have the following equations:
1x + 2y + 3z = 5
3x + 1y + 4.32z = 7
5x + 5y + 5 z = 2
What would you do to find the value of x, y, and z?
There are many ways. You can use Gaussian Elimination, LU factorization, etc.. I would set up the equations into matrix format:
[1 2 3 ] [x] [5]
[3 1 4.32] [y] = [7]
[5 5 5 ] [z] [2]
Basically, I'm turning it into an Ax=b setup where A is a 3x3 matrix in this case, and x is your 3x1 matrix of unknowns.
Then, you can do a Gaussian Elimination on matrix A to simplify into a reduced-row echelon format. Basically, that's matrix where the coeffecients related to your x,y,z variables are isolated, so that you have one coeffecient equal to 1 in one column and the rest of the column elements is equal to zero.
In this case, column [1 3 5] in matrix A would ideally be [1 0 0]. If you simplify matrix A this way, then doing the matrix multiplication (matrix A times matrix b) would ideally give you a simplified version of find the values for your x, y, and z unknowns. Depending on what method you use, you can find the values for the unknowns using back-substitution or forward-substitution.
Back-substitution = starting from the bottom equation and moving up to find your unknowns.
Forward-substitution = opposite of above.
DrPizza
Administrator Elite Member Goat Whisperer
Originally posted by: Ionizer86
Linear algebra is awesome! Solving multiple equations, finding a line through two points or a circle through 3. That's some pretty cool stuff that can be done very elegantly with [matrices]
Yeah! A circle through 3 points. I forgot about that one. I'm doing a very brief into to linear algebra for my pre-calculus class. I love the beauty and elegance of linear algebra and want to "con" some of my students into eventually taking it at college. (actually, I want to encourage them to take more challenging classes... and I let them know that as the semester continues, linear algebra can get quite confusing. That's one of those courses where if you get lost for 1 day, you better catch up quickly or catching up and doing well becomes nearly impossible.
I definitely did all that stuff in Algebra 2 (when I was 14 years old) and I didn't think it was that bad at all.
I always hated working with matrices so I used substitution. Or my TI-82
They teach this stuff AFTER calculus??!?!?!?
I always hated working with matrices so I used substitution. Or my TI-82
They teach this stuff AFTER calculus??!?!?!?
If you are planning to develop games it's a good thing to know. For business programming it's useless.
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