Linear Methods of AI
Matrices, vectors, decompositions, and projections for reading data structure and building linear models.
Definition of Determinant
Determinant Calculation
Laplace Expansion Theorem
Cramer's Rule
Complex Vector Space
Complex Matrix
Eigenvalues, Eigenvectors, and Eigenspaces
Characteristic Polynomial
Eigenvalues of Diagonal and Triangular Matrices
Orthogonal and Unitary Matrices
Symmetric and Hermitian Matrices
Positive Definite Matrix
Scalar Product
Matrix Condition
LU Decomposition
Cholesky Decomposition
QR Decomposition
Linear Model
System of Linear Equations
Linear Equilibrium Problem
Normal Equation System
Normal Equation System Solution
Identifiability and Ranking Capability
Regularization
Statistical Analysis
Best Approximation in Function and Polynomial Spaces
Orthogonal Projection
Orthogonal Polynomials
Matrix Similarity
Matrix Diagonalization
Basic Procedure for Diagonalization
Spectral Theorem
Spectral Theorem for Complex Matrices
Spectral Theorem for Real Matrices
Real Axis Transformation
Principal Component Analysis
Triangularization and Jordan Normal Form
Numerical Calculation of Eigenvalues
Individual Eigenvalue Calculation
All Eigenvalues Calculation
AI Programming
Python, NumPy, control flow, data structures, and coding patterns for data analysis and AI workflows.
Markdown and Command Line Interfaces
First Steps in Python
Everything is an Object in Python
Numbers
Arithmetic Operators
Number Attributes and Methods
Mathematical Functions
Variables
Comparison and Logic
String Objects
Escape Sequence
Indexing and Slicing
String Methods
Print Function
String Formatting
Containers
Immutable, Mutable, and Identity
Iterables
Control Flow
File Input and Output
Dictionary
Functions
Creating Arrays with NumPy
Attributes and Data Types with NumPy
Indexing and Slicing with NumPy
Array Operations with NumPy
Syntactic Sugar