Intro
Table of Contents
About the Author
About the Technical Reviewer
Introduction
Chapter 1: Mathematical Foundations
Linear Algebra
Vector
Scalar
Matrix
Tensor
Matrix Operations and Manipulations
Addition of Two Matrices
Subtraction of Two Matrices
Product of Two Matrices
Transpose of a Matrix
Dot Product of Two Vectors
Matrix Working on a Vector
Linear Independence of Vectors
Rank of a Matrix
Identity Matrix or Operator
Determinant of a Matrix
Interpretation of Determinant
Inverse of a Matrix
Norm of a Vector

Pseudo-Inverse of a Matrix
Unit Vector in the Direction of a Specific Vector
Projection of a Vector in the Direction of Another Vector
Eigen Vectors
Characteristic Equation of a Matrix
Power Iteration Method for Computing Eigen Vector
Calculus
Differentiation
Gradient of a Function
Successive Partial Derivatives
Hessian Matrix of a Function
Maxima and Minima of Functions
Rules for Maxima and Minima for a Univariate Function
Local Minima and Global Minima
Positive Semi-definite and Positive Definite
Convex Set
Convex Function
Non-convex Function

Multivariate Convex and Non-convex Functions Examples
Taylor Series
Probability
Unions, Intersection, and Conditional Probability
Chain Rule of Probability for Intersection of Event
Mutually Exclusive Events
Independence of Events
Conditional Independence of Events
Bayes Rule
Probability Mass Function
Probability Density Function
Expectation of a Random Variable
Variance of a Random Variable
Skewness and Kurtosis
Covariance
Correlation Coefficient
Some Common Probability Distribution
Uniform Distribution
Normal Distribution

Multivariate Normal Distribution
Bernoulli Distribution
Binomial Distribution
Poisson Distribution
Beta Distribution
Dirichlet Distribution
Gamma Distribution
Likelihood Function
Maximum Likelihood Estimate
Hypothesis Testing and p Value
Formulation of Machine-Learning Algorithm and Optimization Techniques
Supervised Learning
Linear Regression as a Supervised Learning Method
Linear Regression Through Vector Space Approach
Classification
Hyperplanes and Linear Classifiers
Unsupervised Learning
Reinforcement Learning

Optimization Techniques for Machine-Learning Gradient Descent
Gradient Descent for a Multivariate Cost Function
Contour Plot and Contour Lines
Steepest Descent
Stochastic Gradient Descent
Newton's Method
Linear Curve
Negative Curvature
Positive Curvature
Constrained Optimization Problem
A Few Important Topics in Machine Learning
Dimensionality-Reduction Methods
Principal Component Analysis
When Will PCA Be Useful in Data Reduction?
How Do You Know How Much Variance Is Retained by the Selected Principal Components?
Singular Value Decomposition