Answer to Question #166501 in Linear Algebra for Marsh

Question

Applications of linear algebra in computer science

Answer 1

Linear algebra is the study of vectors, vector space, linear equations, linear transformation and system of vector matrices. Therefore, vector and matrices are the two main elements that linear algebra is built on. Here are some out of many applications of linear algebra to computer.

(a). Graphics: Pretty much all graphics innovation since computers have existed have come from video and movies. The central part of graphics is projecting a 3D scene into a 2D screen. Projection is already a linear mapping. On top of that, rotations, scaling and perspective are all implemented and analyzed properly using linear algebra.

(b). Facial recognition: A cool way for doing automated facial recognition uses a linear algebraic technique called "principal component analysis". Essentially, this makes use of eigen vectors to rebuild images.

(c). Prediction: The simplest models of prediction are linear models, and these are developed and understood with linear algebra.

Also, linear algebra provides concepts that are crucial to many areas of computer science including, cryptography, machine learning, optimization, quantum computation, web search e.t.c.