Overview
- Gives a unified overview of various phenomena with linear structure from the perspective of functional analysis
- Makes it enjoyable to learn linear algebra with Python by performing linear calculations without manual calculations
- Handles large data such as images and sound using Python and deepens the understanding of linear structures
Part of the book series: Springer Undergraduate Texts in Mathematics and Technology (SUMAT)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
- Orthogonal Projection
- Fourier Expansion
- Generalized Inverse
- Singular Value Decomposition
- Tensor Product
- One-Parameter Semigroup
- Matrix Representation
- Jordan Normal Form
- Peron-Frobenius Theorem
- Dynamical System
- Markov Chain
- Markov Random Field
- KL Expansion
- Kalman Filter
- Jupyter Notebook
- NumPy
- Matplotlib
- Spectral Radius
- SymPy
- VPython
About this book
This textbook is for those who want to learn linear algebra from the basics. After a brief mathematical introduction, it provides the standard curriculum of linear algebra based on an abstract linear space. It covers, among other aspects: linear mappings and their matrix representations, basis, and dimension; matrix invariants, inner products, and norms; eigenvalues and eigenvectors; and Jordan normal forms. Detailed and self-contained proofs as well as descriptions are given for all theorems, formulas, and algorithms.
A unified overview of linear structures is presented by developing linear algebra from the perspective of functional analysis. Advanced topics such as function space are taken up, along with Fourier analysis, the Perron–Frobenius theorem, linear differential equations, the state transition matrix and the generalized inverse matrix, singular value decomposition, tensor products, and linear regression models. These all provide a bridge to more specialized theories based on linear algebra in mathematics, physics, engineering, economics, and social sciences.
Python is used throughout the book to explain linear algebra. Learning with Python interactively, readers will naturally become accustomed to Python coding. By using Python’s libraries NumPy, Matplotlib, VPython, and SymPy, readers can easily perform large-scale matrix calculations, visualization of calculation results, and symbolic computations. All the codes in this book can be executed on both Windows and macOS and also on Raspberry Pi.Authors and Affiliations
About the authors
Makoto Tsukada has been studied in the field of functional analysis. He has been teaching linear algebra, analysis, and probability theory for many years. Also, he has taught programming language courses using Pascal, Prolog, C, Python, etc. Yuji Kobayashi, Hiroshi Kaneko, Sin-Ei Takahasi, Kiyoshi Shirayanagi, and Masato Noguchi are specialists in algebra, analysis, statistics, and computers.
Bibliographic Information
Book Title: Linear Algebra with Python
Book Subtitle: Theory and Applications
Authors: Makoto Tsukada, Yuji Kobayashi, Hiroshi Kaneko, Sin-Ei Takahasi, Kiyoshi Shirayanagi, Masato Noguchi
Series Title: Springer Undergraduate Texts in Mathematics and Technology
DOI: https://doi.org/10.1007/978-981-99-2951-1
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023
Hardcover ISBN: 978-981-99-2950-4Published: 07 December 2023
Softcover ISBN: 978-981-99-2953-5Due: 07 January 2024
eBook ISBN: 978-981-99-2951-1Published: 06 December 2023
Series ISSN: 1867-5506
Series E-ISSN: 1867-5514
Edition Number: 1
Number of Pages: XV, 309
Number of Illustrations: 27 b/w illustrations, 64 illustrations in colour
Topics: Linear Algebra, Functional Analysis, Python