Linear Algebra with Python
Theory and Applications
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Beschreibung
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.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.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
Autor*in
Makoto Tsukada
Themen in »Linear Algebra with Python«
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