비전공자의 인공지능 고군분투기

MIT Gilbert Strang교수님의 Linear Algebra 18강 Properties of Determinants 리뷰입니다. DeterminantsThe determinant is a number associated with any square matrix; det A or |A|determinant는 any square matrix와 연관되어 있는 숫자로써, det A 혹은 |A|로 표기한다.The matrix is invertible exactly when the determinant is non-zero.행렬은 행렬식이 0이 아닐 때 invertible하다.  Properties모든 크기의 정방행렬의 행렬식에 대한 공식을 줄 것이다.특징으로는 아래와 같다. 1. det I = 1 2. 행..

MIT Gilbertsrang 교수님의 Linear algebra 17강 Orthogonal Matrices and Gram-Schmidt 배우겠습니다. Orthonormal Vectors (직교벡터) : 길이가 1인 모든 열벡터가 서로 직교하는 것All have (normal) length 1 and are perpendicular (ortho) to each other. Orthonormal vectors are always independent. 모두 (정규) 길이가 1이고 서로 수직이다. 직교 벡터는 항상 독립적이다. 나아가, Orthonormal vector = orthogonal and unit vector 이다. 즉 every q is orthogonal to every other q.이다...

오늘은 MIT Gilbertstrang 교수님의 Linearalgebra 16강 Projection matrices and least squares를 배우겠습니다.Projections(사영)If b is perpendicular to the column space, then it’s in the left nullspace N(AT) of A and Pb = 0. If b is in the column space then b = Ax for some x, and Pb = b. 1. perpendicular한 경우 : b가 column space에 수직이라면 Pb = 0이다. (vectors in the left nullspace of AT)2) column space 안에 있는 경우 : b가 column ..

MIT Gilberstrang 교수님의 Linear Algebra 15강 Projections onto Subspaces 강의 Projections (투영) : 하나의 vector를 다른 vector로 옮겨 표현하는 것We can see from Figure 1 that this closest point p is at the intersection formed by a line through b that is orthogonal to a. If we think of p as an approximation of b, then the length of e = b − p is the error in that approxi­mation. We could try to find p using trigonometry..

MIT GilbertStrang 교수님의 Linearalgebra 14강 Orthogonal Vectors and subspacesThe “big picture” of this course is that the row space of a matrix’ is orthog­onal to its nullspace, and its column space is orthogonal to its left nullspace.Row space & nullspace는 orthogonal(직교)한다. Column space & left nullspace도 orthogonal(직교)한다.Orthogonal vectors (직교 벡터)Orthogonal is just another word for perpendicular. T..

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 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 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, 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 ..