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

8.5 Problems

Problem 1. Let G = (V,E) be a directed graph and let u,v ∈V be two of its nodes. Show that if there exists a walk from u to v, then there exists a walk without repeated edges and repeated vertices.

Problem 2. Let G = (V,E) be a strongly connected directed graph. Show that jEj ≥jV j, where jSj denotes the number of elements in the set S. (In other words, show that in order to be strongly connected, G must have at least as many edges as nodes.)

Problem 3. Let A ∈ℝ^n×n be an irreducible matrix. Is A² also reducible? (If yes, prove it. If no, show a counterexample.)

Problem 4. Let A ∈ℝ^4×4 be the matrix defined by

⌊ ⌋ | 0 0 1 0| | 0 0 0 1| A = || || . |⌈ 1 0 0 0|⌉ 0 1 0 0

Find the permutation matrix P that transforms A to a Frobenius normal form!

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