Gentle Introduction to Linear Algebra, with Spectacular Applications

This is not a traditional tutorial on linear algebra. The material presented here, in a compact style, is rarely taught in college classes. It covers a wide range of topics, while avoiding excessive use of jargon or advanced math. The fundamental tool is the power of a matrix, and its byproduct, the characteristic polynomial. It can solve countless problems, as discussed later in this article, with illustrations. In the end, it has more to do with calculus, than matrix algebra.

Figure: Auto-regressive models, classified based on the type of roots of the characteristic polynomial

This simple introduction to matrix theory offers a refreshing perspective on the subject. Using a basic concept that leads to a simple formula for the power of a matrix, I show how it can solve time series, Markov chains, linear regression, linear recurrence equations, pseudo-inverse matrices, data reduction, principal components analysis (PCA) and other machine learning problems. These problems are usually solved with more advanced matrix algebra, including eigenvalues, diagonalization, generalized inverse matrices, and other types of matrix normalization.

This article is unusually short despite the wide spectrum of topics covered: only 8 pages long. Read the full article here.