Copyright
Contents
Preface
I Introduction
Welcome
Who Is This Book For?
About Your Outcomes
How to Read This Book
About the Book Structure
About Python Code Examples
About Further Reading
About Getting Help
Summary
II Foundations
Introduction to Linear Algebra
Tutorial Overview
Linear Algebra
Numerical Linear Algebra
Linear Algebra and Statistics
Applications of Linear Algebra
Further Reading
Summary
Linear Algebra and Machine Learning
Reasons to NOT Learn Linear Algebra
Learn Linear Algebra Notation
Learn Linear Algebra Arithmetic
Learn Linear Algebra for Statistics
Learn Matrix Factorization
Learn Linear Least Squares
One More Reason
Summary
Examples of Linear Algebra in Machine Learning
Overview
Dataset and Data Files
Images and Photographs
One Hot Encoding
Linear Regression
Regularization
Principal Component Analysis
Singular-Value Decomposition
Latent Semantic Analysis
Recommender Systems
Deep Learning
Summary
III NumPy
Introduction to NumPy Arrays
Tutorial Overview
NumPy N-dimensional Array
Functions to Create Arrays
Combining Arrays
Extensions
Further Reading
Summary
Index, Slice and Reshape NumPy Arrays
Tutorial Overview
From List to Arrays
Array Indexing
Array Slicing
Array Reshaping
Extensions
Further Reading
Summary
NumPy Array Broadcasting
Tutorial Overview
Limitation with Array Arithmetic
Array Broadcasting
Broadcasting in NumPy
Limitations of Broadcasting
Extensions
Further Reading
Summary
IV Matrices
Vectors and Vector Arithmetic
Tutorial Overview
What is a Vector
Defining a Vector
Vector Arithmetic
Vector Dot Product
Vector-Scalar Multiplication
Extensions
Further Reading
Summary
Vector Norms
Tutorial Overview
Vector Norm
Vector L1 Norm
Vector L2 Norm
Vector Max Norm
Extensions
Further Reading
Summary
Matrices and Matrix Arithmetic
Tutorial Overview
What is a Matrix
Defining a Matrix
Matrix Arithmetic
Matrix-Matrix Multiplication
Matrix-Vector Multiplication
Matrix-Scalar Multiplication
Extensions
Further Reading
Summary
Types of Matrices
Tutorial Overview
Square Matrix
Symmetric Matrix
Triangular Matrix
Diagonal Matrix
Identity Matrix
Orthogonal Matrix
Extensions
Further Reading
Summary
Matrix Operations
Tutorial Overview
Transpose
Inverse
Trace
Determinant
Rank
Extensions
Further Reading
Summary
Sparse Matrices
Tutorial Overview
Sparse Matrix
Problems with Sparsity
Sparse Matrices in Machine Learning
Working with Sparse Matrices
Sparse Matrices in Python
Extensions
Further Reading
Summary
Tensors and Tensor Arithmetic
Tutorial Overview
What are Tensors
Tensors in Python
Tensor Arithmetic
Tensor Product
Extensions
Further Reading
Summary
V Factorization
Matrix Decompositions
Tutorial Overview
What is a Matrix Decomposition
LU Decomposition
QR Decomposition
Cholesky Decomposition
Extensions
Further Reading
Summary
Eigendecomposition
Tutorial Overview
Eigendecomposition of a Matrix
Eigenvectors and Eigenvalues
Calculation of Eigendecomposition
Confirm an Eigenvector and Eigenvalue
Reconstruct Matrix
Extensions
Further Reading
Summary
Singular Value Decomposition
Tutorial Overview
What is the Singular-Value Decomposition
Calculate Singular-Value Decomposition
Reconstruct Matrix
Pseudoinverse
Dimensionality Reduction
Extensions
Further Reading
Summary
VI Statistics
Introduction to Multivariate Statistics
Tutorial Overview
Expected Value and Mean
Variance and Standard Deviation
Covariance and Correlation
Covariance Matrix
Extensions
Further Reading
Summary
Principal Component Analysis
Tutorial Overview
What is Principal Component Analysis
Calculate Principal Component Analysis
Principal Component Analysis in scikit-learn
Extensions
Further Reading
API
Articles
Summary
Linear Regression
Tutorial Overview
What is Linear Regression
Matrix Formulation of Linear Regression
Linear Regression Dataset
Solve via Inverse
Solve via QR Decomposition
Solve via SVD and Pseudoinverse
Solve via Convenience Function
Extensions
Further Reading
Summary
VII Appendix
Getting Help
Linear Algebra on Wikipedia
Linear Algebra Textbooks
Linear Algebra University Courses
Linear Algebra Online Courses
NumPy Resources
Ask Questions About Linear Algebra
How to Ask Questions
Contact the Author
How to Setup a Workstation for Python
Overview
Download Anaconda
Install Anaconda
Start and Update Anaconda
Further Reading
Summary
Linear Algebra Cheat Sheet
Array Creation
Vectors
Matrices
Types of Matrices
Matrix Operations
Factorization
Statistics
Basic Math Notation
Tutorial Overview
The Frustration with Math Notation
Arithmetic Notation
Greek Alphabet
Sequence Notation
Set Notation
Other Notation
Tips for Getting More Help
Further Reading
Summary
VIII Conclusions
How Far You Have Come