Linear Algebra

In this chapter, we will be covering the main concepts of linear algebra, and the concepts learned here will serve as the backbone on which we will learn all the concepts in the chapters to come, so it is important that you pay attention. 

It is very important for you to know that these chapters cannot be substituted for an education in mathematics; they exist merely to help you better grasp the concepts of deep learning and how various architectures work and to develop an intuition for why that is, so you can become a better practitioner in the field.

At its core, algebra is nothing more than the study of mathematical symbols and the rules for manipulating these symbols. The field of algebra acts as a unifier for all of mathematics and provides us with a way of thinking. Instead of using numbers, we use letters to represent variables. 

Linear algebra, however, concerns only linear transformations and vector spaces. It allows us to represent information through vectors, matrices, and tensors, and having a good understanding of linear algebra will take you a long way on your journey toward getting a very strong understanding of deep learning. It is said that a mathematical problem can only be solved if it can be reduced to a calculation in linear algebra. This speaks to the power and usefulness of linear algebra.

This chapter will cover the following topics:

• Comparing scalars and vectors
• Linear equations
• Matrix operations
• Vector spaces and subspaces
• Linear maps
• Matrix decompositions