Basic Linear Algebra for Deep Learning

The concepts of Linear Algebra are crucial for understanding the theory behind Machine Learning, especially for Deep Learning.

They give you better intuition for how algorithms really work under the hood, which enables you to make better decisions. So if you really want to be a professional in this field, you cannot escape mastering some of its concepts. This post will give you an introduction to the most important concepts of Linear Algebra that are used in Machine Learning. 

Introduction

Linear Algebra is a continuous form of mathematics and is applied throughout science and engineering because it allows you to model natural phenomena and to compute them efficiently. Because it is a form of continuous and not discrete mathematics, a lot of computer scientists don’t have a lot of experience with it. Linear Algebra is also central to almost all areas of mathematics like geometry and functional analysis. Its concepts are a crucial prerequisite for understanding the theory behind Machine Learning, especially if you are working with Deep Learning Algorithms. You don’t need to understand Linear Algebra before getting started with Machine Learning, but at some point, you may want to gain a better understanding of how the different Machine Learning algorithms really work under the hood. This will help you to make better decisions during a Machine Learning system’s development. So if you really want to be a professional in this field, you will have to master the parts of Linear Algebra that are important for Machine Learning. In Linear Algebra, data is represented by linear equations, which are presented in the form of matrices and vectors. Therefore, you are mostly dealing with matrices and vectors rather than with scalars (we will cover these terms in the following section). When you have the right libraries, like Numpy, at your disposal, you can compute complex matrix multiplication very easily with just a few lines of code. (Note: this blog post ignores concepts of Linear Algebra that are not important for Machine Learning.)

Mathematical Objects

Scalar

A scalar is simply a single number. For example 24.

Vector

A Vector is an ordered array of numbers and can be in a row or a column. A Vector has just a single index, which can point to a specific value within the Vector. For example, V2 refers to the second value within the Vector, which is -8 in the graphic above.

Matrix

A Matrix is an ordered 2D array of numbers and it has two indices. The first one points to the row and the second one to the column. For example, M23 refers to the value in the second row and the third column, which is 8 in the yellow graphic above. A Matrix can have multiple numbers of rows and columns. Note that a Vector is also a Matrix, but with only one row or one column. […]

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