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

Other Books You May Enjoy

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

6.5 Problems

Problem 1. Compute the eigenvalues of the matrices

⌊ ⌋ ⌊ ⌋ | 4 1 − 1| | 2 1 1| A = |⌈ 1 3 1 |⌉ , B = |⌈ 1 2 1|⌉, − 1 1 2 1 1 2

and find an eigenvector for every eigenvalue.

Problem 2. Let A ∈ℝ^n×n be an upper or lower triangular matrix. Show that the eigenvalues of A are its diagonal elements.

Problem 3. Let A ∈ℝ^n×n be a square matrix. Show that

det(A − λI )

is a polynomial of degree n in λ.

This is the characteristic polynomial that we have talked about, and we have even mentioned this fact. However, we omitted the proof, so here’s your chance to fill the gap.

Problem 4. Let A ∈ℝ^n×n, B ∈ℝ^n×m, and C ∈ℝ^m×m arbitrary matrices, and we define the so-called block matrix

⌊ ⌋ ⌈A B ⌉ (n+m )× (n+m ) D = 0 C ∈ ℝ .

Show that if λ is an eigenvalue of A or an eigenvalue of B, then it’s also an eigenvalue of C.

Join our community on Discord

Read this book alongside other users, Machine Learning experts, and the author himself. Ask questions, provide solutions to other readers, chat with...