# Thread: applications of linear algebra

1. ## applications of linear algebra

Hello,
I just finished linear algebra I course which was full of theory, now I want to see some application of linear algebra, can you tell what are the applications of linear algebra? I am most interested in the field of computer science.

Thanks.

2. There are tons of applications of linear algebra. Perhaps the most direct ones I have found are in quantum mechanics, without which there would be no computers. Other applications include solving the gigantic algebraic systems that arise from finite element analysis (500k x 500k systems are quite commonplace) numerical solutions of pde's. For example: you want to design the landing gear for a Boeing aircraft. But you don't want to have to build and test it physically, because that's expensive. So, you model it with finite element analysis. The result is the large linear system you must solve. You use techniques of linear algebra to solve the system. Numerical analysis, indeed, is part of the intersection of math and cs (courses, for example, are often cross-listed).

You can use linear algebra to solve problem in theoretical cs like the number of walks of length n in a directed graph (turns into an eigenvalue problem). You can use linear algebra to solve problems in optimization of processor time in operating systems. The list goes on and on. Probably the only field of mathematics with more applications than linear algebra is calculus.

3. Originally Posted by Mansel
I am choosing math courses and am curious as to know which one is better/easier?
Course Descriptions:
Matrix algebra: including vectors and matrices, linear equations, determinants
Linear Algebra: Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces; orthogonality; eigenvalues and eigenvectorsHomework help...
First, don't "hijack" someone else's thread for a completely separate question- start your own.

Second, "matrix algebra" is a very specific, concrete course. It will involve a lot of calculation, very little theory. "Linear algebra" is much more broad and involves a lot of theory. Strictly speaking, matrix algebra is a subfield of linear algebra.

4. Originally Posted by Ginsburg
Hello,
I just finished linear algebra I course which was full of theory, now I want to see some application of linear algebra, can you tell what are the applications of linear algebra? I am most interested in the field of computer science.

Thanks.
One application that comes to mind immediately is this: the set of all solutions to an nth order, linear, homogeneous differential equation forms a vector space. I'm no expert on computer science but most computational problems can be most simply expressed in terms of matrices.