선형대수
1.[선형대수] Lecture 1: The geometry of linear equations (선형방정식의 기하학)
강의 링크: https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/$$2{x} - {y} = 0 \\tag{1}$$ $$\-x + 2y = 3 \\t
2.[선형대수] Lecture 2: Elimination with matrices
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/lecture-2-elimination-with-matrices/$${x} + 2{y} + z = 2$$ $$3{x} + 8{y} +
3.[선형대수] Lecture 3: Multiplication and inverse matrices
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/먼저, 이전 강의에서 진행한 내용을 복습해보자.$$\\underbrace{\\begin{bmat
4.[선형대수] Lecture 4: Factorization into A = LU
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/먼저 Inverse Matrix에서 시작한다.$$AA^{-1} = I = A^{-1}A$$위 수
5.[선형대수] Lecture 5: Transposes, permutations, spaces R^n
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/우리는 이전 강의에서 $A=LU$ 꼴로 만드는 방법을 배웠다.그리고 이 과정에서 Eliminat
6.[선형대수] Lecture 6: Column space and nullspace
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/먼저 vector space에 대한 정의는 다음과 같다. ($v, w$: vector, $c,
7.[선형대수] Lecture 7: Solving Ax = 0: pivot variables, special solutions
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이전 강의에서 nullspace에 대해서 배웠다.그렇다면 $Ax=0$에서 벡터 x를 어떻게 컴퓨
8.[선형대수] Lecture 8: Solving Ax = b: row reduced form R
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/"어떻게 $Ax=b$에 대한 값을 찾을 수 있을까."해당 강의는 위 내용에 대해서 다룬다.먼저
9.[선형대수] Lecture 9: Independence, basis, and dimension
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/$$A : m\\times n$$위와 같은 행렬 $A$는 방정식보다 변수의 수가 더 많을 것이다
10.[선형대수] Lecture 10: The four fundamental subspaces
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/오늘은 "4 Fundmental Subspaces"에 대해서 알아본다.$A:m\\times n$
11.[선형대수] Lecture 11: Matrix spaces; rank 1; small world graphs
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/$$M=\\text{all 3$\\times$3 matrices}$$위와 같이 3x3 크기를 갖
12.[선형대수] Lecture 12: Graphs, networks, incidence matrices
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/그래프는 노드와 엣지들의 집합이다.$$Graph = {nodes, \\ edges}$$예시로 다
13.[선형대수] Lecture 14: Orthogonal vectors and subspaces
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/먼저 다음과 같이 정리를 하고, 이후 증명을 한다.$$dim(row \\ space) : r$$
14.[선형대수] Lecture 15: Projections onto subspaces
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/먼저 vector projection에 대해서 알아보자.위 그래프처럼 벡터 $a,b \\in \
15.[선형대수] Lecture 16: Projection matrices and least squares
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/지난번 강의에서 $Ax=b$에서 벡터 $b$를 subspace $C(A)$에 project하여,
16.[선형대수] Lecture 17: Orthogonal matrices and Gram-Schmidt
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/먼저 강의에서 다음과 같은 내용을 정리한다.$$\\text{<orthonormal vect
17.[선형대수] Lecture 18: Properties of determinants
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 determination의 properties(특징)들에 대해서 배운다.dete
18.[선형대수] Lecture 19: Determinant formulas and cofactors
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/지난 강의에서 determinations의 properties에 대해서 배웠다.$$\\det(I
19.[선형대수] Lecture 20: Cramer's rule, inverse matrix, and volume
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 다음과 같은 내용을 다룬다.$$\\text{1. Formula for $A^{-
20.[선형대수] Lecture 21: Eigenvalues and eigenvectors
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 "Eigenvalues and Eigenvectors"에 대해서 배운다.$\\d
21.[선형대수] Lecture 22: Diagonalization and powers of A
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 다음 내용을 다룬다."Diagonalization a matrix $S^{-1}
22.[선형대수] Lecture 23: Differential equations and exp(At)
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/오늘 강의에서 배울 내용은 다음과 같다.Differential Equations $\\frac{
23.[선형대수] Lecture 24: Markov matrices; fourier series
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 다음과 같은 내용을 배운다.Markov matrices (steday state
24.[선형대수] Lecture 25: Symmetric matrices and positive definiteness
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 다음과 같은 내용을 배운다.Symmetric matrices's Eigenval
25.[선형대수] Lecture 26: Complex matrices; fast fourier transform
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 다음 내용을 배운다.Complex vectors, matrices 의 inner
26.[선형대수] Lecture 27: Positive definite matrices and minima
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 다음과 같은 내용을 다룬다.Postiive Definite Matrix증명 방법
27.[선형대수] Lecture 28: Similar matrices and Jordan form
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 다음과 같은 내용을 다룬다.Similar Matrices ($B=M^{-1}AM
28.[선형대수] Lecture 29: Singular value decomposition
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 다음과 같은 내용을 다룬다.Singular Value Decomposition
29.[선형대수] Lecture 30: Linear transformations and their matrices
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 다음과 같은 내용을 배운다.Linear Transforamtion $T$Cons
30.[선형대수] Lecture 31: Change of basis; image compression
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/해당 강의에서는 다음과 같은 내용을 배운다.change of basiscompression of
31.[선형대수] Lecture 33: Left and right inverses; pseudoinverse
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/이번 강의에서는 다음과 같은 내용을 다룬다.About 4 subspaces (rowspace,