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안녕하세요오늘은Lecture11 Matrix Spaces; Rank 1; Small World Graphs 에 대해 학습하겠습니다.  Matrix spaces (New vector spaces)New vector spaces = Matrix spaces, M = all 3 by 3 matrices새로운 벡터공간은 행렬 공간이며, M은 모든 3 * 3 행렬이다.또한, 행렬 M은 3가지 부분 공간인 Symmetric Matrix, Upper triangular Matrix, Diagonal Matrix를 가지고 있다.Dimension & BasisThe dimension of M is 9; we must choose 9 numbers to specify an element of M. The space M i..

안녕하세요,오늘은 MIT Gilbert Strang 교수님의 Linear algebra 10강 four fundamental subspaces에 대해 학습하겠습니다.  Four subspacesAny m by n matrix A determines four subspaces (possibly containing only the zero vector):Column space, C(A)C(A) consists of all combinations of the columns of A and is a vector space in Rm.C(A)는 A의 열의 모든 조합으로 구성되며 Rm의 벡터 공간이다. Nullspace, N(A)This consists of all solutions x of the equation..

안녕하세요,오늘은 9강 Independence, Basis and Dimension에 대해 학습하겠습니다. Linear independence : Vector가 있을 때, 모든 계수(coefficient)가 0인 경우를 제외하고, 선형 조합(Linear combination)으로도 0을 만들 수 없다면 이 벡터들은 독립(independent)하다고 한다.A combination of the columns is zero, so the columns of this A are dependent.열의 A 조합이 0이라면, A의 열은 종속(depdendent)이 된다.We say vectors x1,x2,...xn are linearly independent (or just independent) if c1x1 ..

오늘은 MIT GilbertStrang교수님의 Linear algebra 8강에 대해 학습하겠습니다.Solvability conditions on bThe third row of A is the sum of its first and second rows, so we know that if Ax = b the third component of b equals the sum of its first and second components. If b does not satisfy b3 = b1 + b2 the system has no solution. If a combination of the rows of A gives the zero row, then the same combination of the ent..

안녕하세요,오늘은 MIT Gilbert Strang교수님의 Linear algebra 6강 Column Space and Nullspace에 대해 리뷰해보도록 하겠습니다.   Vector SpaceA vector space is a collection of vectors which is closed under linear combinations. In other words, for any two vectors v and w in the space and any two real numbers c and d, the vector cv + dw is also in the vector space. A subspace is a vector space contained inside a vector space. Ve..

안녕하세요, 오늘은 MIT 선형대수(Linear algebra) 5강 Transposes, permutations, vector spaces에 대해 학습해보겠습니다.   Permutations(치환)Multiplication by a permutation matrix치환행렬은 행교환 (row exchange)을 수행하는 행렬이다. 행교환은 pivot이 0인 경우에 반드시 필요하다. P swaps the rows of a matrix; when applying the method of elimination we use permutation matrices to move ze­ros out of pivot positions. Our factorization A = LU then becomes PA = LU,..

안녕하세요, 오늘은 MT Gilbert Strang 교수님의 Linear Algebra 수업 Lecture4, Factorization into A = LU 에 대해 다루어보겠습니다.      Inverse of a productThe inverse of a matrix product AB is B−1 A−1. AB의 역행렬은 B−1 A−1이다.  Transpose of a product행과 열을 바꿀 때 사용the entry in row i column j of A is the entry in row j column i of A^T열I와 행J의 A를 열J와 행I으로 바꾼 것을 A^T라고 한다. The transpose of a matrix product AB is BTAT. For any invert..

안녕하세요 오늘은 MIT Gilbert Strang교수님의 Linear algebra 3강 Multiplication and Inverse Matrices를 공부하도록 하겠습니다. Matrix A multiplying 1. Column Combination행*열의 곱을 원소별 계산으로 정리할 수 있다. (대부분은 벡터로 표현)If they are square, they have got to be the same.If they are rectangular, they are not the same size.here goes A, again, times B producing C.A times a vector is a combination of the columns of A.because the columns ..

안녕하세요, 오늘은 MIT Gilbert Strang교수님의 선형대수 강의 Lecture#2 Elimination with Matrices로 공부해보도록 하겠습니다.  Method of EliminationElimination is the technique most commonly used by computer software to solve systems of linear equations. It finds a solution x to Ax = b whenever the matrix A is invertible. In the example used in class,The number 1 in the upper left corner of A is called the first pivot.The first..

안녕하세요, 인공지능 전공자라면 정말 중요하지만 어렵게 느끼는 선형대수학 입니다. 오늘은 MIT GilbertStrang 교수님의 2강인 An Overview of Linear Algebra 에 대해 리뷰해보겠습니다.   This is an overview of linear algebra given at the start of a course on the math­ ematics of engineering.  VectorsWhat do we do with vectors? Take combinationsWe can multiply vectors by scalars(such as under x1,x2,x3), add, and subtract. Given vectors u, vand w we can form ..