You're reading from Mathematics of Machine Learning Master linear algebra, calculus, and probability for machine learning

Product type Paperback

Published in May 2025

Publisher Packt

ISBN-13 9781837027873

Length 730 pages

Edition 1st Edition

Concepts

Machine Learning

Author (1):

Tivadar Danka

View More author details

Table of Contents (36) Chapters

Introduction

Part 1: Linear Algebra FREE CHAPTER

1 Vectors and Vector Spaces

2 The Geometric Structure of Vector Spaces

3 Linear Algebra in Practice

4 Linear Transformations

5 Matrices and Equations

6 Eigenvalues and Eigenvectors

7 Matrix Factorizations

8 Matrices and Graphs

References

Part 2: Calculus

9 Functions

10 Numbers, Sequences, and Series

11 Topology, Limits, and Continuity

12 Differentiation

13 Optimization

14 Integration

References

Part 3: Multivariable Calculus

15 Multivariable Functions

16 Derivatives and Gradients

17 Optimization in Multiple Variables

References

Part 4: Probability Theory

18 What is Probability?

19 Random Variables and Distributions

20 The Expected Value

References

Part 5: Appendix

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Index

Appendix A It’s Just Logic

1. Appendix B The Structure of Mathematics

2. Appendix C Basics of Set Theory

3. Appendix D Complex Numbers

4.3 Linear transformations in the Euclidean plane

We have just seen that a linear transformation can be described by the image of a basis set. From a geometric viewpoint, they are functions mapping parallelepipeds to parallelepipeds.

Because of the linearity, you can imagine this as distorting the grid determined by the bases.

Figure 4.6: How linear transforms distort the grid determined by the basis vectors

In two dimensions, we have seen a few examples of geometric maps such as scaling and rotation as linear transformations. Now we can put them into matrix form. There are five of them in particular that we will study: stretching, shearing, rotation, reflection, and projection.

These simple transformations are not only essential to build intuition, but they are also frequently applied in computer vision. Flipping, rotating, and stretching are essential parts of image augmentation pipelines, greatly enhancing the performance of models.