Linear Algebra Coding with Python: Python's application for linear algebra

Book Synopsis: Python is one of the most popular languages for data analysis and prediction. What's more, tensorflow and torch, useful tools of recent deep learning, are fully implemented by Python. The basic form of data in these languages is an array, created by Python's important package numpy. In particular, arrays are the basis of data science because they have structures of vectors and matrices that give the meaning of direction and magnitude to each value in the data set. For example, a matrix structure allows transformation to a simple form without losing the basic characteristics of a vast data set. These transformations are useful for efficient processing of data and for finding implicit characteristics.

Linear Algebra, a field that provides a basic theory of the usefulness of vectors and matrices, provides many algorithms to increase the accuracy and speed of computation in the computational process for analyzing data and to discover the characteristics of a data set. These algorithms are very useful for understanding the computing process of probability, statistics and the learning machine.

This book introduces many basics of linear algebra using Python packages numpy, sympy, and so on. Chapters 1 and 2 introduce the creation and characteristics of vectors and matrices. Chapter 3 describes the linear system through the process of calculating the solution in a system of simultaneous equations. Space, a concept introduced in Chapter 4, is used to infer the collective characteristics and relationships of each vector of a linear system. Chapter 5 introduces the coordinate system to represent the linear system geometrically. Chapter 6 introduces the process of transforming while maintaining basic characteristics such as vectors and matrices. Finally, Chapter 7 describes several ways to decompose the original form into a simple form. In this process, we use a variety of Python functions.