#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

# Introduction

A matrix is a rectangular array of numbers or expressions arranged in rows and columns and considered as a single entity. As we are considering a matrix as a single object, if we perform an operation on it, it will apply to each of the elements within it:

Figure 6.1: A simple m × n matrix with m rows and n columns

A simple linear single-dimension array rarely suffices for the physical world we live in, and almost all attributes related to space and time require more than one dimension. Compactness is one of the main reasons for the use of matrices. A matrix is compact when it is closed and bounded or simply has its points within a fixed distance of one another. Primarily for these two reasons, matrices find applications in practically every field, including fundamental mathematical concepts, ranging from graph theory, linear transformations, and probability theory, to different branches of physics, such as quantum mechanics and electromagnetism...