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Mathematics of Machine Learning

Mathematics of Machine Learning

By : Tivadar Danka
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Mathematics of Machine Learning

Mathematics of Machine Learning

3 (2)
By: Tivadar Danka

Overview of this book

Mathematics of Machine Learning provides a rigorous yet accessible introduction to the mathematical underpinnings of machine learning, designed for engineers, developers, and data scientists ready to elevate their technical expertise. With this book, you’ll explore the core disciplines of linear algebra, calculus, and probability theory essential for mastering advanced machine learning concepts. PhD mathematician turned ML engineer Tivadar Danka—known for his intuitive teaching style that has attracted 100k+ followers—guides you through complex concepts with clarity, providing the structured guidance you need to deepen your theoretical knowledge and enhance your ability to solve complex machine learning problems. Balancing theory with application, this book offers clear explanations of mathematical constructs and their direct relevance to machine learning tasks. Through practical Python examples, you’ll learn to implement and use these ideas in real-world scenarios, such as training machine learning models with gradient descent or working with vectors, matrices, and tensors. By the end of this book, you’ll have gained the confidence to engage with advanced machine learning literature and tailor algorithms to meet specific project requirements. *Email sign-up and proof of purchase required
Table of Contents (36 chapters)
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2
Part 1: Linear Algebra
11
References
12
Part 2: Calculus
19
References
20
Part 3: Multivariable Calculus
24
References
25
Part 4: Probability Theory
29
References
30
Part 5: Appendix
31
Other Books You May Enjoy
32
Index

6.4 Summary

In this chapter, we’ve veered into the theory side of math once again. This time, it was about eigenvalues and eigenvectors of a matrix, that is, scalars λ and vectors x for which

 n×n Ax = λx, A ∈ ℝ

hold.

Just like most mathematical objects, this might seem daunting at first, but geometrically, this means that in the direction x, the linear transformation A is the same as a stretching by λ. In practice, we can find eigenvectors by solving the so-called characteristic equation

det(A − λI) = 0

for λ.

What are eigenvalues used for? There are tons of applications, but one stands out: according to Theorem 38, if you can build a basis from the eigenvectors of the matrix A n×n, then you can find a T n×n such that T1AT is diagonal. This process is extremely useful. For one, multiplication with diagonal matrices is fast and simple, and we prefer to do it whenever we can. For another, diagonalization reveals a ton about the internal...

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