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Practical Linear Algebra for Data Science

Mike X Cohen
promocja -15%
cena: 299 zł 254.15 zł
Data wydania: 2022-09-06
stron: 328, miĂŞkka oprawa, format:

więcej na stronie helion.pl

Practical Linear Algebra for Data Science eBook -- spis treści

  • Preface
    • Conventions Used in This Book
    • Using Code Examples
    • OReilly Online Learning
    • How to Contact Us
    • Acknowledgments
  • 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
        • The geometry of vector-scalar multiplication
      • 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
        • Linear weighted combinations
        • Geometric transforms
    • Matrix Operations: Transpose
      • Dot and Outer Product Notation
    • Matrix Operations: LIVE EVIL (Order of Operations)
    • Symmetric Matrices
      • Creating Symmetric Matrices from Nonsymmetric Matrices
    • Summary
    • Code Exercises
  • 6. Matrices, Part 2
    • Matrix Norms
      • Matrix Trace and Frobenius Norm
    • Matrix Spaces (Column, Row, Nulls)
      • Column Space
      • Row Space
      • Null Spaces
    • Rank
      • Ranks of Special Matrices
      • Rank of Added and Multiplied Matrices
      • Rank of Shifted Matrices
      • Theory and Practice
    • Rank Applications
      • In the Column Space?
      • Linear Independence of a Vector Set
    • Determinant
      • Computing the Determinant
      • Determinant with Linear Dependencies
      • The Characteristic Polynomial
    • Summary
    • Code Exercises
  • 7. Matrix Applications
    • Multivariate Data Covariance Matrices
    • Geometric Transformations via Matrix-Vector Multiplication
    • Image Feature Detection
    • Summary
    • Code Exercises
      • Covariance and Correlation Matrices Exercises
      • Geometric Transformations Exercises
      • Image Feature Detection Exercises
  • 8. Matrix Inverse
    • The Matrix Inverse
    • Types of Inverses and Conditions for Invertibility
    • Computing the Inverse
      • Inverse of a 2 × 2 Matrix
      • Inverse of a Diagonal Matrix
      • Inverting Any Square Full-Rank Matrix
      • One-Sided Inverses
    • The Inverse Is Unique
    • Moore-Penrose Pseudoinverse
    • Numerical Stability of the Inverse
    • Geometric Interpretation of the Inverse
    • Summary
    • Code Exercises
  • 9. Orthogonal Matrices and QR Decomposition
    • Orthogonal Matrices
    • Gram-Schmidt
    • QR Decomposition
      • Sizes of Q and R
        • Why is upper triangular
      • QR and Inverses
    • Summary
    • Code Exercises
  • 10. Row Reduction and LU Decomposition
    • Systems of Equations
      • Converting Equations into Matrices
      • Working with Matrix Equations
    • Row Reduction
      • Gaussian Elimination
      • Gauss-Jordan Elimination
      • Matrix Inverse via Gauss-Jordan Elimination
    • LU Decomposition
      • Row Swaps via Permutation Matrices
    • Summary
    • Code Exercises
  • 11. General Linear Models and Least Squares
    • General Linear Models
      • Terminology
      • Setting Up a General Linear Model
    • Solving GLMs
      • Is the Solution Exact?
      • A Geometric Perspective on Least Squares
      • Why Does Least Squares Work?
    • GLM in a Simple Example
    • Least Squares via QR
    • Summary
    • Code Exercises
  • 12. Least Squares Applications
    • Predicting Bike Rentals Based on Weather
      • Regression Table Using statsmodels
      • Multicollinearity
      • Regularization
    • Polynomial Regression
    • Grid Search to Find Model Parameters
    • Summary
    • Code Exercises
      • Bike Rental Exercises
      • Multicollinearity Exercise
      • Regularization Exercise
      • Polynomial Regression Exercise
      • Grid Search Exercises
  • 13. Eigendecomposition
    • Interpretations of Eigenvalues and Eigenvectors
      • Geometry
      • Statistics (Principal Components Analysis)
      • Noise Reduction
      • Dimension Reduction (Data Compression)
    • Finding Eigenvalues
    • Finding Eigenvectors
      • Sign and Scale Indeterminacy of Eigenvectors
    • Diagonalizing a Square Matrix
    • The Special Awesomeness of Symmetric Matrices
      • Orthogonal Eigenvectors
      • Real-Valued Eigenvalues
    • Eigendecomposition of Singular Matrices
    • Quadratic Form, Definiteness, and Eigenvalues
      • The Quadratic Form of a Matrix
      • Definiteness
      • T Is Positive (Semi)definite
    • Generalized Eigendecomposition
    • Summary
    • Code Exercises
  • 14. Singular Value Decomposition
    • The Big Picture of the SVD
      • Singular Values and Matrix Rank
    • SVD in Python
    • SVD and Rank-1 Layers of a Matrix
    • SVD from EIG
      • SVD of T
      • Converting Singular Values to Variance, Explained
      • Condition Number
    • SVD and the MP Pseudoinverse
    • Summary
    • Code Exercises
  • 15. Eigendecomposition and SVD Applications
    • PCA Using Eigendecomposition and SVD
      • The Math of PCA
      • The Steps to Perform a PCA
      • PCA via SVD
    • Linear Discriminant Analysis
    • Low-Rank Approximations via SVD
      • SVD for Denoising
    • Summary
    • Exercises
      • PCA
      • Linear Discriminant Analyses
      • SVD for Low-Rank Approximations
      • SVD for Image Denoising
  • 16. Python Tutorial
    • Why Python, and What Are the Alternatives?
    • IDEs (Interactive Development Environments)
    • Using Python Locally and Online
      • Working with Code Files in Google Colab
    • Variables
      • Data Types
      • Indexing
    • Functions
      • Methods as Functions
      • Writing Your Own Functions
      • Libraries
      • NumPy
      • Indexing and Slicing in NumPy
    • Visualization
    • Translating Formulas to Code
    • Print Formatting and F-Strings
    • Control Flow
      • Comparators
      • If Statements
        • elif and else
        • Multiple conditions
      • For Loops
      • Nested Control Statements
    • Measuring Computation Time
    • Getting Help and Learning More
      • What to Do When Things Go Awry
    • Summary
  • Index



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