Linear Algebra with Python : Theory and Applications / by Makoto Tsukada, Yuji Kobayashi, Hiroshi Kaneko, Sin-Ei Takahasi, Kiyoshi Shirayanagi, Masato Noguchi.

Format:

Book

Author/Creator:

Tsukada, Makoto.

Contributor:

Kobayashi, Yūji.

Kaneko, Hiroshi.

Takahasi, Sin-Ei.

Shirayanagi, Kiyoshi.

Noguchi, Masato.

Series:

Springer Undergraduate Texts in Mathematics and Technology, 1867-5514

Language:

English

Subjects (All):

Algebras, Linear.

Functional analysis.

Python (Computer program language).

Linear Algebra.

Functional Analysis.

Python.

Local Subjects:

Linear Algebra.

Functional Analysis.

Python.

Physical Description:

1 online resource (315 pages)

Edition:

1st ed. 2023.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2023.

Summary:

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.

Contents:

Mathematics and Python

Linear Spaces and Linear Mappings

Basis and Dimension

Matrices

Elementary Operations and Matrix Invariants

Inner Product and Fourier Expansion

Eigenvalues and Eigenvectors

Jordan Normal Form and Spectrum

Dynamical Systems

Applications and Development of Linear Algebra.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

981-9929-51-2

OCLC:

1415896905