Linear Algebra with Python Theory and Applications 1st Edition by Makoto Tsukada, Yugi Kobayashi, Hiroshi Kaneko, Sin Ei Takahasi, Kiyoshi Shirayanagi, Masato Noguchi ISBN 9789819929511

Linear Algebra with Python Theory and Applications 1st Edition by Makoto Tsukada, Yugi Kobayashi, Hiroshi Kaneko, Sin Ei Takahasi, Kiyoshi Shirayanagi, Masato Noguchi – Ebook PDF Instant Download/Delivery: 9789819929511
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ISBN 10: 
ISBN 13: 9789819929511
Author: Makoto Tsukada, Yugi Kobayashi, Hiroshi Kaneko, Sin Ei Takahasi, Kiyoshi Shirayanagi, Masato Noguchi

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.

Linear Algebra with Python Theory and Applications 1st Edition Table of contents:

Chapter 1: Introduction to Linear Algebra and Python
1.1 What is Linear Algebra?
1.2 The Role of Linear Algebra in Mathematics and Science
1.3 Why Python for Linear Algebra?
1.4 Installing Python and Required Libraries
1.5 Overview of Key Python Libraries for Linear Algebra (NumPy, SciPy, Matplotlib)
1.6 Structure of the Book

Chapter 2: Vectors and Vector Spaces
2.1 Defining Vectors
2.2 Vector Operations in Python
2.3 Linear Combinations and Span
2.4 Vector Spaces and Subspaces
2.5 Basis and Dimension
2.6 Implementing Vector Space Concepts in Python
2.7 Python Code Examples: Vector Operations and Visualizations

Chapter 3: Matrices and Matrix Operations
3.1 Introduction to Matrices
3.2 Matrix Addition, Scalar Multiplication, and Transposition
3.3 Matrix Multiplication and Its Properties
3.4 The Inverse and Determinant of a Matrix
3.5 Rank of a Matrix
3.6 Python Implementation: Matrix Operations and Visualization
3.7 Solving Linear Systems Using Matrices

Chapter 4: Linear Transformations
4.1 What Are Linear Transformations?
4.2 Matrix Representation of Linear Transformations
4.3 Eigenvalues and Eigenvectors
4.4 Diagonalization of Matrices
4.5 Applications of Linear Transformations
4.6 Python Code: Visualizing Transformations and Eigenvectors

Chapter 5: Systems of Linear Equations
5.1 Introduction to Linear Systems
5.2 Methods for Solving Linear Systems: Gaussian Elimination and Substitution
5.3 The Matrix Approach to Solving Systems
5.4 The LU Decomposition
5.5 Python Solutions for Linear Systems
5.6 Using NumPy to Solve Systems of Linear Equations
5.7 Applications of Solving Linear Systems

Chapter 6: Determinants and Their Applications
6.1 The Concept of Determinants
6.2 Computing Determinants for 2×2 and 3×3 Matrices
6.3 Properties of Determinants
6.4 Applications of Determinants in Solving Linear Systems
6.5 Python Implementation for Determinants
6.6 The Cramer’s Rule and Its Python Application

Chapter 7: Eigenvalues and Eigenvectors
7.1 The Eigenvalue Problem
7.2 Finding Eigenvalues and Eigenvectors
7.3 The Characteristic Equation
7.4 Diagonalization of Matrices and Its Applications
7.5 The Spectral Theorem for Symmetric Matrices
7.6 Python Code for Finding Eigenvalues and Eigenvectors
7.7 Applications: Principal Component Analysis (PCA)

Chapter 8: Inner Product Spaces
8.1 Introduction to Inner Product Spaces
8.2 The Dot Product and Its Properties
8.3 Orthogonality and Orthonormality
8.4 Gram-Schmidt Process
8.5 Applications of Inner Products in Geometry and Physics
8.6 Python Implementation for Inner Products and Orthogonality

Chapter 9: Singular Value Decomposition (SVD)
9.1 Introduction to Singular Value Decomposition
9.2 The Mathematical Foundation of SVD
9.3 SVD and Its Applications
9.4 Low-Rank Approximation and Data Compression
9.5 Python Code: Performing SVD in Python
9.6 Applications: Image Compression and Latent Semantic Analysis (LSA)

Chapter 10: Applications of Linear Algebra
10.1 Linear Algebra in Data Science and Machine Learning
10.2 Applications in Physics and Engineering
10.3 Linear Algebra in Computer Graphics
10.4 Solving Optimization Problems Using Linear Algebra
10.5 Python Applications in Real-World Problems
10.6 Case Study: Predictive Modeling with Linear Algebra

Chapter 11: Numerical Methods for Linear Algebra
11.1 Introduction to Numerical Linear Algebra
11.2 Numerical Stability and Floating-Point Arithmetic
11.3 Direct and Iterative Methods for Solving Linear Systems
11.4 The Role of Matrix Factorizations in Numerical Methods
11.5 Eigenvalue Computation Using Iterative Methods
11.6 Python Libraries for Numerical Linear Algebra (SciPy, NumPy)

Chapter 12: Advanced Topics in Linear Algebra
12.1 Advanced Matrix Factorizations: QR and Cholesky Decomposition
12.2 The Schur Decomposition and Its Applications
12.3 Linear Algebra in Optimization and Game Theory
12.4 Introduction to Tensor Decompositions
12.5 Python Code Examples for Advanced Topics

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Makoto Tsukada,Yugi Kobayashi,Hiroshi Kaneko,Sin Ei Takahasi,Kiyoshi Shirayanagi,Masato Noguchi,Linear Algebra,Python