Can anyone explain the purposes of linear algebra?

[jmcoreymv]

Back in highschool when I learned calculus, the uses of calculus were very obvious. For example, derivatives let you find rate of change of something, integrals can give you a position from a velocity, etc..

But I never learned what the purposes of linear algebra were really. I know there's all types of special matrices and matrix operations, determinants, eigenvalues and vectors, etc, but how do these apply to solve real problems? I'm taking a class that covers pattern classification and we are calculating things like eigenvalues, but I don't quite see the link.

 

[radioouman]

One application of matrices is finite element analysis. Linear algebra let's you solve a matrix.

 

[SpecialEd]

Linear algebra is the theory behind linear functions on vector spaces. If you are interested in solving systems of equations involving several variables you will need a solid background in linear algbrea.

 

[Itchrelief]

I believe they are very heavily used in 3d computing. If you wish to go into that field you better know some matrix math. The computer will do the calculation but you should know the theory so you know how to set it up.

 

[dullard]

x + 3y = 10
2y + x/2 = 0

Find x and y. That is linear algebra at its most simple state. It gives you the tools to quickly and easilly solve multiple equations for multiple variables. You've been doing this since ~7th grade. If you haven't seen a use for it yet, I say you should stay out of any mathematics, engineering, or science field.

 

[jmcoreymv]

Originally posted by: dullard
x + 3y = 10
2y + x/2 = 0

Find x and y. That is linear algebra at its most simple state. It gives you the tools to quickly and easilly solve multiple equations for multiple variables. You've been doing this since ~7th grade. If you haven't seen a use for it yet, I say you should stay out of any mathematics, engineering, or science field.

I guess I phrased my question poorly. Can you explain what knowing the eigenvalues and vectors are and how they relate to solving problems?

 

[SpecialEd]

Originally posted by: jmcoreymv

Originally posted by: dullard
x + 3y = 10
2y + x/2 = 0

Find x and y. That is linear algebra at its most simple state. It gives you the tools to quickly and easilly solve multiple equations for multiple variables. You've been doing this since ~7th grade. If you haven't seen a use for it yet, I say you should stay out of any mathematics, engineering, or science field.

I guess I phrased my question poorly. Can you explain what knowing the eigenvalues and vectors are and how they relate to solving problems?

If you are given a map from a vector space to itself, one question you can ask is what subspaces are fixed by that map. The eigen vectors are exactly those subspaces fixed and the eigen values tell you in what way they are fixed.

Knowing the eigen values and eigen spaces is the most effective way of understanding a linear map.