This repository contains my tutorials on how to master Matrix operation and numerical optimisation with Eigen and C++. The following will be the outline of this repository:
- Matrix Class
- Vector Class
- Array Class
- Initialization
- Accessing Elements (Coefficient)
- Reshaping, Resizing, Slicing
- Tensor Module
- Matrix Arithmetic
- Coefficient-Wise Operations
- Reductions
- Minimum/ Maximum Element In The Matrix
- Minimum/ Maximum Element Row-wise/Col-wise in the Matrix
- Sum Of All Elements
- Mean Of The Matrix
- Mean Of The Matrix Row-wise/Col-wise
- The Trace Of The Matrix
- The Multiplication Of All Elements
- Norm 2 of The Matrix
- Norm Infinity Of The Matrix
- Checking If All Elements Are Positive
- Checking If Any Elements Is Positive
- Counting Elements
- Matrix Condition Number
- Matrix Rank
- Broadcasting
- Memory Alignment
- Passing Eigen objects by value to functions
- Aliasing
- Memory Mapping
- Unary Expression
- Eigen Functor
- Introduction to Linear Equation
- Vector space
- Introduction to Linear Equation
- Solving Linear Equation
- Row echelon form
- Reduced row echelon form
- Trapezoidal Matrix
- Matrices Decompositions
- Linear Map
- Span
- Subspace
- Row Spaces and Column Spaces
- Range of a Matrix
- Basis
- Rank of Matrix
- Dimension of the Column Space
- Null Space (Kernel)
- Nullity
- Rank-nullity Theorem
- The Determinant of The Matrix
- Finding The Inverse of The Matrix
- The Fundamental Theorem of Linear Algebra
- Permutation Matrix
- Augmented Matrix