作者：(荷)迈克·X.科恩(Mike X Co
页数：311页
出版社：东南大学出版社
出版日期：2023
ISBN：9787576605884
电子书格式：pdf/epub/txt
内容简介
如果你想从事计算或技术领域的工作，理解线性代数是少不了的。线性代数的研究对象是矩阵及其运算，是几乎所有计算机算法和分析的数学基础。但它在几十年前的教科书中的呈现方式与专业人员如今用来解决现实世界问题的方式有很大不同。这本来自Mike X Cohen的实用指南讲授了以Python实现的线性代数的核心概念，包括如何在数据科学、机器学习、深度学习、计算模拟和生物医学数据处理应用中使用它们。有了这本书，理解、实现和适应繁多的现代分析方法和算法将不再是问题。
作者简介
迈克·X.科恩是荷兰唐德斯研究所（拉德堡德大学医学中心）的神经科学副教授。他在科学编程、数据分析、统计学和相关主题的教学方面拥有20多年的经验，并且已经创作了多门在线课程和教材。Mike身上有一种冷幽默感，喜欢紫色的东西。
目录
Preface
1. Introduction
What Is Linear Algebra and Why Learn It
About This Book
Prerequisites
Math
Attitude
Coding
Mathematical Proofs Versus Intuition from Coding
Code, Printed in the Book and Downloadable Online
Code Exercises
How to Use This Book (for Teachers and Self Learners)
2. Vectors, Part 1
Creating and Visualizing Vectors in NumPy
Geometry of Vectors
Operations on Vectors
Adding Two Vectors
Geometry of Vector Addition and Subtraction
Vector-Scalar Multiplication
Scalar-Vector Addition
Transpose
Vector Broadcasting in Python
Vector Magnitude and Unit Vectors
The Vector Dot Product
The Dot Product Is Distributive
Geometry of the Dot Product
Other Vector Multiplications
Hadamard Multiplication
Outer Product
Cross and Triple Products
Orthogonal Vector Decomposition
Summary
Code Exercises
3. Vectors, Part 2
Vector Sets
Linear Weighted Combination
Linear Independence
The Math of Linear Independence
Independence and the Zeros Vector
Subspace and Span
Basis
Definition of Basis
Summary
Code Exercises
4. Vector Applications
Correlation and Cosine Similarity
Time Series Filtering and Feature Detection
k-Means Clustering
Code Exercises
Correlation Exercises
Filtering and Feature Detection Exercises
k-Means Exercises
5. Matrices, Part 1
Creating and Visualizing Matrices in NumPy
Visualizing, Indexing, and Slicing Matrices
Special Matrices
Matrix Math: Addition, Scalar Multiplication, Hadamard Multiplication
Addition and Subtraction
“Shifting” a Matrix
Scalar and Hadamard Multiplications
Standard Matrix Multiplication
Rules for Matrix Multiplication Validity
Matrix Multiplication
Matrix-Vector Multiplication
Matrix Operations: Transpose
……
6. Matrices, Part 2
7. Matrix Applications
8. Matrix Inverse
9. Orthogonal Matrices and QR Decomposition
10. Row Reduction and LU Decomposition
11. General Linear Models and Least Squares
12. Least Squares Applications
13. Eigendecomposition
14. Singular Value Decomposition
15. Eigendecomposition and SVD Applications
16. Python Tutorial
1. Introduction
What Is Linear Algebra and Why Learn It
About This Book
Prerequisites
Math
Attitude
Coding
Mathematical Proofs Versus Intuition from Coding
Code, Printed in the Book and Downloadable Online
Code Exercises
How to Use This Book (for Teachers and Self Learners)
2. Vectors, Part 1
Creating and Visualizing Vectors in NumPy
Geometry of Vectors
Operations on Vectors
Adding Two Vectors
Geometry of Vector Addition and Subtraction
Vector-Scalar Multiplication
Scalar-Vector Addition
Transpose
Vector Broadcasting in Python
Vector Magnitude and Unit Vectors
The Vector Dot Product
The Dot Product Is Distributive
Geometry of the Dot Product
Other Vector Multiplications
Hadamard Multiplication
Outer Product
Cross and Triple Products
Orthogonal Vector Decomposition
Summary
Code Exercises
3. Vectors, Part 2
Vector Sets
Linear Weighted Combination
Linear Independence
The Math of Linear Independence
Independence and the Zeros Vector
Subspace and Span
Basis
Definition of Basis
Summary
Code Exercises
4. Vector Applications
Correlation and Cosine Similarity
Time Series Filtering and Feature Detection
k-Means Clustering
Code Exercises
Correlation Exercises
Filtering and Feature Detection Exercises
k-Means Exercises
5. Matrices, Part 1
Creating and Visualizing Matrices in NumPy
Visualizing, Indexing, and Slicing Matrices
Special Matrices
Matrix Math: Addition, Scalar Multiplication, Hadamard Multiplication
Addition and Subtraction
“Shifting” a Matrix
Scalar and Hadamard Multiplications
Standard Matrix Multiplication
Rules for Matrix Multiplication Validity
Matrix Multiplication
Matrix-Vector Multiplication
Matrix Operations: Transpose
……
6. Matrices, Part 2
7. Matrix Applications
8. Matrix Inverse
9. Orthogonal Matrices and QR Decomposition
10. Row Reduction and LU Decomposition
11. General Linear Models and Least Squares
12. Least Squares Applications
13. Eigendecomposition
14. Singular Value Decomposition
15. Eigendecomposition and SVD Applications
16. Python Tutorial
