저자

Kwangmin Kim

공개

2100년 03월 01일

1 Contents

1.1 Basic

2023-03-23, Variable types
2023-03-14, Harmonic Mean
2026-05-05, Closed Form, Functional Form, Canonical Form
1111-11-11, Function
- 2023-01-31, Function
- 2023-01-31, Function (1) - Univariable Scalar Function (One to One)
- 2023-01-31, Function (2) - Multi-variable Scalar Function (Many to One)
- 2023-01-31, Function (3) - Univariable Vector Function (One to Many)
- 2023-01-31, Function (4) - Multi-variable Vector Function (Many to Many)
- 2023-02-18, Function (5) - Composite Function
- 2026-03-23, Function (6) - 함수의 합 vs 합성함수 — Sequential vs Joint 추정
2023-02-18, Transformations of Functions
2023-03-24, Convex Combination
2023-03-18, Higher Order Derivative
2023-03-15, Minimizer & Minimum
2023-03-15, Taylor Series
1111-11-11, Vector & Matrix
2023-03-14, Limit, \(\epsilon-\delta\) Method
Differentiation
- 2023-02-04, Derivative (1) - Univariable Scalar Funtion
- 2023-02-10, Derivative (2) - Chain Rule & Partial Derivative
- 1111-11-11, Derivative (3) - Higher Order Derivative
- 1111-11-11, Derivative (4) - Mean Value Theorem
- 1111-11-11, Derivative (5) - Gradient
2023-03-15, Talyer’s Series
1111-11-11, Gradient Direction
1111-11-11, Random Variable
1111-11-11, Probability Distribution
1111-11-11, Information Theory - Entropy
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1.2 Linear Algebra

1.2.1 MIT 18.06 Linear Algebra (Gilbert Strang) 강의 시리즈

2026-04-08, MIT 18.06 코스 전체 개요 — 왜 배우는가, 무엇을 다루는가

1.2.1.1 Ch.1 Introduction to Vectors

2026-04-06, Ch.1 Overview — 선형결합, 내적, 코사인, 노름 종류
2026-04-06, Ch.1 §1.1 — Vectors and Linear Combinations
2026-04-08, Ch.1 §1.2 — Lengths and Dot Products

1.2.1.2 Ch.2 Solving Linear Equations

2026-04-08, Ch.2 Overview — Row Picture · Column Picture · Ax=b에서 LU 분해까지
2026-04-08, Ch.2 §2.1 — Vectors and Linear Equations
2026-04-08, Ch.2 §2.2 — The Idea of Elimination
2026-04-08, Ch.2 §2.3 — Elimination Using Matrices
2026-04-08, Ch.2 §2.4 — Rules for Matrix Operations
2026-04-08, Ch.2 §2.6 — Elimination = Factorization: A = LU
2026-04-08, Ch.2 §2.7 — Transposes and Permutations

1.2.1.3 Ch.3 Vector Spaces and Subspaces

2026-04-09, Ch.3 §3.1 — Spaces of Vectors and Subspaces Overview
2026-04-09, Ch.3 §3.1 심화 — Spaces of Vectors (행렬·다항식·함수 공간, 부분공간 교집합·합)
2026-04-09, Ch.3 §3.2 — The Nullspace of A: Solving Ax = 0
2026-04-09, Ch.3 §3.3 — The Rank and the Row Reduced Form
2026-04-09, Ch.3 §3.4 — The Complete Solution to Ax = b
2026-04-09, Ch.3 §3.5 — Independence, Basis and Dimension
2026-04-09, Ch.3 §3.6 — Dimensions of the Four Subspaces
2023-03-30, Special Matrices — 카탈로그 (정사각·대각·대칭·멱등·중심행렬·공분산)
2026-04-12, \(X^\top X\) 가 왜 분산인가 — Gram Matrix, Scatter Matrix, 공분산 행렬

1.2.1.4 Ch.4 Orthogonality

2026-04-10, Ch.4 Overview — 직교성(Orthogonality) 개요
2026-04-10, Ch.4 §4.1 — Orthogonality of the Four Subspaces
2026-04-10, Ch.4 §4.2 — Projections (투영)
2026-04-10, Ch.4 §4.3 — Least Squares Approximations (최소제곱 근사)
2026-04-10, Ch.4 §4.4 — Orthogonal Bases and Gram-Schmidt (정규직교 기저와 그람-슈미트)

1.2.1.5 Ch.5 Determinants

2026-04-10, Ch.5 Overview — Determinants (행렬식) 개요
2026-04-10, Ch.5 §5.1 — The Properties of Determinants (행렬식의 성질)
2026-04-10, Ch.5 §5.2 — Permutations and Cofactors (순열과 여인수)
2026-04-10, Ch.5 §5.3 — Cramer’s Rule, Inverses, and Volumes (크래머 공식·역행렬·부피)

1.2.1.6 Ch.6 Eigenvalues and Eigenvectors

1.2.1.7 Ch.7 Linear Transformations

1.2.1.8 Ch.9 Numerical Linear Algebra

1.2.2 응용/확장 토픽

2023-04-02, Matrix Calculus — 행렬·벡터 미분 공식
2026-04-11, Singular Value Decomposition (SVD)
2026-04-11, Linear Transformations (심화) — 개요 포스트 참조
2026-04-12, Ch.8 Applications — 선형대수의 7가지 응용 종합 개요
2026-04-12, Ch.8 §8.1 Matrices in Engineering — 강성행렬 \(K = A^\top C A\) 와 차분-물성-균형
2026-04-12, Ch.8 §8.2 Graphs and Networks — 접속행렬·키르히호프 법칙·그래프 라플라시안
2026-04-12, Ch.8 §8.3 Markov Matrices, Population, and Economics — Perron-Frobenius·Leslie·Leontief
2026-04-12, Ch.8 §8.4 Linear Programming — 부등식·최소화가 선형대수를 만났을 때
2026-04-12, Ch.8 §8.5 Fourier Series — 함수 공간에서의 선형대수
2026-04-12, Ch.8 §8.6 Linear Algebra for Statistics and Probability — 가중 최소제곱·공분산·PCA
2026-04-12, Ch.8 §8.7 Computer Graphics — 동차 좌표와 4×4 행렬의 세계

1.3 Graph Theory

2026-03-24, 그래프 이론 기초
1111-11-11, 그래프 알고리즘 심화 (SCC, 위상 정렬, 최소 신장 트리)
1111-11-11, 그래프 임베딩 (Node2Vec, GNN)

1.4 Optimization

2023-03-23, Minimizer & Minimum
1111-11-11, Convex Set
1111-11-11, Convex Function
1111-11-11, Unconstrained Optimization
1111-11-11, Non-linear Least Square
1111-11-11, Largrange Multiplier Method
- 1111-11-11, Largrange Primal Function
- 1111-11-11, Largrange Dual Function
- 1111-11-11, KKT conditions
1111-11-11, Gradient Descent Optimizers
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