Welcome to this course on elementary matrix methods. The field of linear algebra is used to model many real-world processes, for instance, we can model text documents to project them into three space or into multidimensional space in order to see which documents are related to which other documents. We can model the evolution of the flu virus and other processes and bioinformatics, for instance, here, we look at the embedding of the flu virus genetic sequence data into two space and see a nice progression. We can model anything that can be represented as tabular data, for instances, nutrition matrix that shows the nutrition values of various foods, and we can model our activities in vision and navigation using linear algebra, for instance, we can model a picture as a matrix of numbers. This is a fast-paced course that we'll explore any elementary properties of matrices and as tabular data and as mathematical objects. We will illustrate some of these properties using some real life situations which can be modeled as matrices. We will begin by talking of matrices as a linear map and look at how to translate, say menu into nutrition items, as an example, we will look at reversing this process in getting a system of linear equations and spaces, we will look at linear least squares, which on orthogonality, which comes when you have too many variables and you cannot fit an exact solution, and we will end with the singular value decomposition, which is a fundamental tool used in many applications in statistics and machine learning. The fundamental building block in linear algebra are matrices. You can think of a matrix as a table, so a table with n rows and p columns forms an n by p matrix. But, we will see in this course that matrices are much more than just tables. They are mathematical objects that can be combined and manipulated using certain mathematical rules that we will explore. As an example, as a mathematical object, we will see the matrices represent linear mappings. For instance, the process of going from a point in three space to a two-dimensional representation of a three space known as a map is a linear mapping. So, if you move along a straight line in three space, you would trace a straight line in a two space map.
