TITLE: How does linear algebra help with computer science?
QUESTION [22 upvotes]: 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?

REPLY [9 votes]: Linear algebra applies to many areas of machine learning. Here is just a small set of examples.

Support Vector Machines find a best separating hyperplane between two sets of vectors. The optimization problem minimizes an objective function that is most clearly expressed using linear algebra, the minimization algorithms are often solved in the dual space using linear algebra, and proofs regarding the algorithms involve linear algebra.
Many semi-supervised label propagation graph algorithms can be expressed as optimization of formulae involving the graph's Laplacian matrix.
Spectral clustering separates data points into groups of related points by finding the eigenvalues of a graph's Laplacian matrix that have small eigenvectors.
Neural nets use linear algebra in various ways. For example, densely connected neural net layers perform matrix/tensor multiplication to propagate values between them.
Convex optimization algorithms, which are used throughout machine learning, use linear algebra. The most common algorithm is Low-Memory BFGS.
Optimization algorithms used for non-convex problems, such as AdaGrad, are often formulated and implemented using linear algebra.