Brownlee J. Basics of Linear Algebra for Machine Learning. Discover the Mathematical Language of Data in Python

New York: Jason Brownlee., 2018. — 212 p.Linear algebra is a pillar of machine learning. You cannot develop a deep understanding and application of machine learning without it. In this new laser-focused Ebook written in the friendly Machine Learning Mastery style that you’re used to, you will finally cut through the equations, Greek letters, and confusion, and discover the topics in linear algebra that you need to know.
Using clear explanations, standard Python libraries, and step-by-step tutorial lessons, you will discover what linear algebra is, the importance of linear algebra to machine learning, vector, and matrix operations, matrix factorization, principal component analysis, and much more.
Some classical methods used in the field of linear algebra,such as linear regression via linear least squares and singular-value decomposition are linear algebra methods, and other methods, such as principal component analysis were born from the marriage of linear algebra and statistics. To read and understand machine learning you must be able to read and understand linear algebra. This book helps machine learning practitioners get on top of linear algebra fast.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 HelpFoundations
Introduction to Linear Algebra
Tutorial Overview
Linear Algebra
Numerical Linear Algebra
Linear Algebra and Statistics
Applications of Linear Algebra
Further ReadingLinear 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 ReasonExamples of Linear Algebra in Machine LearningOverviewDataset and Data Files
Images and Photographs
One Hot Encoding
Linear Regression
Regularization
Principal Component Analysis
Singular-Value Decomposition
Latent Semantic Analysis
Recommender Systems
Deep LearningNumPy
Introduction to NumPy Arrays
Tutorial Overview
NumPy N-dimensional Array
Functions to Create Arrays
Combining Arrays
Extensions
Further ReadingIndex, Slice and Reshape NumPy Arrays
Tutorial Overview
From List to Arrays
Array Indexing
Array Slicing
Array Reshaping
Extensions
Further ReadingNumPy Array Broadcasting
Tutorial Overview
Limitation with Array Arithmetic
Array Broadcasting
Broadcasting in NumPy
Limitations of Broadcasting
Extensions
Further ReadingMatrices
Vectors and Vector Arithmetic
Tutorial Overview
What is a Vector
Defining a Vector
Vector Arithmetic
Vector Dot Product
Vector-Scalar Multiplication
Extensions
Further ReadingVector Norms
Tutorial Overview
Vector Norm
Vector L
Norm
Vector L
Norm
Vector Max Norm
Extensions
Further ReadingMatrices 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 ReadingTypes of Matrices
Tutorial Overview
Square Matrix
Symmetric Matrix
Triangular Matrix
Diagonal Matrix
Identity Matrix
Orthogonal Matrix
Extensions
Further ReadingMatrix Operations
Tutorial Overview
Transpose
Inverse
Trace
Determinant
Rank
Extensions
Further ReadingSparse Matrices
Tutorial Overview
Sparse Matrix
Problems with Sparsity
Sparse Matrices in Machine Learning
Working with Sparse Matrices
Sparse Matrices in Python
Extensions
Further ReadingTensors and Tensor Arithmetic
Tutorial Overview
What are Tensors
Tensors in Python
Tensor Arithmetic
Tensor Product
Extensions
Further ReadingFactorization
Matrix Decompositions
Tutorial Overview
What is a Matrix Decomposition
LU Decomposition
QR Decomposition
Cholesky Decomposition
Extensions
Further ReadingEigendecomposition
Tutorial Overview
Eigendecomposition of a Matrix
Eigenvectors and Eigenvalues
Calculation of Eigendecomposition
Confirm an Eigenvector and Eigenvalue
Reconstruct Matrix
Extensions
Further ReadingSingular Value Decomposition
Tutorial Overview
What is the Singular-Value Decomposition
Calculate Singular-Value Decomposition
Reconstruct Matrix
Pseudoinverse
Dimensionality Reduction
Extensions
Further ReadingStatistics
Introduction to Multivariate Statistics
Tutorial Overview
Expected Value and Mean
Variance and Standard Deviation
Covariance and Correlation
Covariance Matrix
Extensions
Further ReadingPrincipal Component Analysis
Tutorial Overview
What is Principal Component Analysis
Calculate Principal Component Analysis
Principal Component Analysis in scikit-learn
Extensions
Further Reading
API
ArticlesLinear 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 ReadingGetting 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 PythonOverviewDownload Anaconda
Install Anaconda
Start and Update Anaconda
Further ReadingLinear 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 ReadingHow Far You Have Come