Introduction
What's the data?
Data Representation
Linear Algebra
Linear system & Matrix : 단일 벡터 / 매트릭스
- Systems of linear equations
- How to solve the linear equations?
Vector space & Linear independence
- What's the vector space?
- What's the linear independence?
- When can utilize the linear independence?
Basis & Rank & Afiine space
- What's basis and rank in vector space?
- What's linear mapping?
Analytic Geometry : 복수 벡터 / 매트릭스
Norms & Angles
- Which types of norms should we consider?
- What's the angle of vectors?
- Applications of norms & angles
Basis
- what's the basis of vector space or matrix?
- Why do we need to know the basis?
- Applications where the basis is utilized
Orthogonality & Rotation
- What's the relation of orthogonality?
- How can we rotate a given vector?
- Applications of orthogonality & rotating
Matrix Decomposition
Eigenvalue & Eigenvector
- What's the eigenvalue & eigenvector?
- What's the relation between the eigenvalue and the eigenvector?
- why do we need the eigenvalue and eigenvector?
Cholesky Decomposition & Diagonalization
- How can we apply Cholesky decomposition to matrix?
- Why do we need to know the diagonalization?
- Applications of diagonalization
Singular Value Decomposition
- What's the singular value decomposition?
- How can we decompose the matrix by SVD?
- Applications of SVD
Vector Calculus
Differentiation & Gradients
- What's the differentiation?
- How can we utilize the gradients?
Higher-order derivatives & Taylor series
- What's the difference between the conventional derivatives and the higher-order derivatives?
- What's Taylor series?
- Applications of derivatives & Taylor series
Probability and Distribution
Probability & Bayes' theorem
- Basics of probability
- What's Bayes' theorem
- Extension of Bayes' theorem
Independence & Exponential family
- What's the independence in probability?
- What's the exponential family?
- Applications of exponential family
Memory Vision