Linear algebra is a field of mathematics that is widely used in various disciplines. The field of data science also leans on many different applications of linear algebra. This does not mean that every data scientist needs to have an extraordinary mathematical background, since the amount of math you will be dealing with depends a lot on your role. However, a good understanding of linear algebra really enhances the understanding of many machine learning algorithms. Foremost, to really understand deep learning algorithms, linear algebra is essential. This article introduces the most important basic linear algebra concepts, and shows two relevant data science applications of linear algebra.

Contents

• Matrices and Vectors
• Matrix Operations
• Matrix Inverse
• Orthogonal Matrix
• Applications of Linear Algebra within Data Science (SVD and PCA)

Matrices and Vectors

In short, we can say that linear algebra is the ‘math of vectors and matrices’. We make use of such vectors and matrices since these are convenient mathematical ways of representing large amounts of information.

A matrix is an array of numbers, symbols or expressions, made up of rows and columns. A matrix is characterized by the amount of rows, m, and the amount of columns, n, it has. In general, a matrix of order ‘m x n’ (read: “m by n”) has m rows and n columns. Below, we display an example 2 x 3 matrix A:

We can refer to individual elements of the matrix through its corresponding row and column. For example, A[1, 2] = 2, since in the first row and second column the number 2 is placed.

A matrix with only a single column is called a vector. For example, every column of the matrix A above is a vector. Let us take the first column of the matrix A as the vector v:

In a vector, we can also refer to individual elements. Here, we only have to make use of a single index. For example, v[2] = 4, since 4 is the second element of the vector v.

Matrix Operations

Our ability to analyze and solve particular problems within the field of linear algebra will be greatly enhanced when we can perform algebraic operations with matrices. Here, the most important basic tools for performing these operations are listed.

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