Linear Algebra with Python: Theory and Applications

This textbook provides a comprehensive introduction to linear algebra, covering topics such as linear mappings, matrices, invariants, eigenvalues, and Jordan normal forms. It is designed for beginners and advanced students and uses Python to demonstrate computational techniques.

Format: Hardback
Length: 309 pages
Publication date: 07 December 2023
Publisher: Springer Verlag, Singapore

This comprehensive textbook is designed to cater to individuals seeking a solid foundation in linear algebra. After providing a brief mathematical introduction, it delves into the standard curriculum of linear algebra, focusing on an abstract linear space. The book encompasses various aspects, including linear mappings and their matrix representations, bases, and dimension; matrix invariants, inner products, and norms; eigenvalues and eigenvectors; and Jordan normal forms. Thorough and self-contained proofs accompany each theorem, formula, and algorithm, ensuring a clear understanding of the subject matter.

To provide a unified perspective on linear structures, the book develops linear algebra from the standpoint of functional analysis. Advanced topics such as function space, Fourier analysis, the Perron–Frobenius theorem, linear differential equations, the state transition matrix, and the generalized inverse matrix are explored. These topics serve as a gateway to more specialized theories rooted in linear algebra, spanning mathematics, physics, engineering, economics, and social sciences.

Throughout the book, Python is employed as the primary language to explain linear algebra. By utilizing Python interactively, readers can develop a comfortable familiarity with Python coding. Through the use of Pythons libraries NumPy, Matplotlib, VPython, and SymPy, readers can effortlessly perform large-scale matrix calculations, visualize the results of these calculations, and engage in symbolic computations. The codes presented in this book are compatible with both Windows and macOS systems, as well as Raspberry Pi, allowing for a wide range of execution environments.

By embracing this textbook, readers will embark on a transformative journey into the world of linear algebra, equipped with the knowledge and tools necessary to excel in various scientific and mathematical disciplines.

Weight: 809g
Dimension: 254 x 178 (mm)
ISBN-13: 9789819929504
Edition number: 1st ed. 2023