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I'm a Computer Science student. I've just completed a linear algebra course. I got 75 points out of 100 points on the final exam. I know linear algebra well. As a programmer, I'm having a difficult time understanding how linear algebra helps with computer science?

Can someone please clear me up on this topic?

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Linear transformations have many applications in graphics. – user10444 Mar 28 '13 at 16:44
@user10444 can you please give me some examples? – Billie Mar 28 '13 at 16:58
A nice way to represent graphs is as an adjacency matrix. Many algorithms use this matrix representation and matrix operation to manipulate the graph. Graphs are absolutely fundamental for computer science. Programming is not computer science. – DanielV Mar 4 at 2:38
up vote 17 down vote accepted

The page Coding The Matrix: Linear Algebra Through Computer Science Applications (see also this page) might be useful here.

In the second page you read among others

In this class, you will learn the concepts and methods of linear algebra, and how to use them to think about problems arising in computer science.

I guess you have been giving a standard course in linear algebra, with no reference to applications in your field of interest. Although this is standard practice, I think that an approach in which the theory is mixed with applications is to be preferred. This is surely what I did when I had to teach Mathematics 101 to Economics majors, a few years ago.

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Good-to-know. thank-you. – Billie Mar 28 '13 at 21:03

Algebra is used in computer science in many ways: boolean algebra for evaluating code paths, error correcting codes, processor optimization, relational database design/optimization, and so forth.

Matrix computations are used in computer programming in many ways: graphics, state-space modeling, arithmetic, ad hoc business logic, and so forth.

Linear algebra as a sub-discipline is often taught in one of two ways: from a computational aspect of things, which focuses on matrices, their properties, and operations on matrices; or, algebraically, where linear mappings are treated as algebraic structures, and one studies, for instance, the group theoretic relations that arise.

In either case, you will not need to try too hard to find situations where knowledge of either theoretical linear algebra or matrix mathematics will be necessary.

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A computer scientist needs various algebraic theories: semigroups, rings, fields, categories. Linear algebra is a base for most of them. Besides, it is used in all other mathematical sciences (differencial equations, probability etc.)

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