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

3.2 Matrices, the workhorses of linear algebra

I am quite sure that you were already familiar with the notion of matrices before reading this book. Matrices are one of the most important data structures that can represent systems of equations, graphs, mappings between vector spaces, and many more. Matrices are the fundamental building blocks of machine learning.

At first look, we define a matrix as a table of numbers. If the matrix A has, for instance, n rows and m columns of real numbers, we write

⌊ ⌋ | a1,1 a1,2 ... a1,m | || a2,1 a2,2 ... a2,m || | . . . . | n×m A = || .. .. .. .. || ∈ ℝ . || a a ... a || ⌈ n,1 n,2 n,m ⌉

(3.1)

When we don’t want to write out the entire matrix as (3.1), we use the abbreviation A = (a_i,j)_i=1,j=1^n,m.

The set of all n ×m real matrices is denoted by ℝ^n×m. We will exclusively talk about real matrices, but when referring to other types, this notation is modified accordingly. For instance, ℤ^{n×m} denotes the set of integer matrices.