A Brief Introduction to Matrix Algebra

Matrix algebra is one of the most useful tools in many disciplines, in particularly those related to data analysis (statistics, signal processing, machine learning, etc.). This short tutorial intends to provide a brief summary of the most important facts relating to matrix algebra for a person that has taken a linear algebra course a long time ago and has forgotten most of the details. Although I did my best to make the text readable even by a complete novice, it is clear that the size of the document does not allow for a comprehensive explanation, so beginners are advised to consult some good fat textbook full of pictures, examples and exercises. This exposition sacrifices a lot of generality for the sake of simplicity, and only covers those topics that were required by a certain course on machine learning.