Mathematics/Linear Algebra 썸네일형 리스트형 LDA (Linear Discriminant Analysis) (일단 설명 잘 되어있고, 예제 있는 참고 자료 투척, PPT) LDA (Linear Discriminant Analysis) 란? LDA seeks to reduce dimensionality while preserving as much of the class discriminatory information as possible 간단하게 말해서... LDA 는 클래스들의 정보를 보호하면서 차원을 최소로 줄이겠다는 얘기다. PCA (Principal Component Analysis) 는 뭐지? PCA 는 한 데이터베이스 안에 여러개의 클래스가 포함되었을때, 클래스의 종류와 상관없이 모든 원소들의 경향을 분석하는 방법이다. 위와 같이 모든 원소들이 어떠한 방향으로 늘어져 있는지를 분석해서 기저백터(V1,.. 더보기 Eigenvalues and eigenvectors, Characteristic polynomial http://en.wikipedia.org/wiki/Eigenvalue,_eigenvector_and_eigenspace The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain parallel to the original vector. For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector is scaled when multiplied by the matrix. The prefix eigen- is adopted from the German word "eig.. 더보기 Cramer’s Formula http://en.wikipedia.org/wiki/Cramer's_rule Consider a system of n linear equations for n unknowns, represented in matrix multiplication form as follows: where the n by n matrix A has a nonzero determinant, and the vector is the column vector of the variables. Then the theorem states that in this case the system has a unique solution, whose individual values for the unknowns are given by: where A.. 더보기 Matrix Algebra http://people.hofstra.edu/Stefan_Waner/RealWorld/Summary3.html Basic Definitions An m×n matrix A is a rectangular array of real numbers with m rows and n columns. (Rows are horizontal and columns are vertical.) The numbers m and n are the dimensions of A. The real numbers in the matrix are called its entries. The entry in row i and column j is called aij or Aij. Example Following is a 4×5 matrix.. 더보기 adjoint matrix, minor, cofactor 소행렬식 = minor 여인자 = cofactor 의 n차의 정사각행렬 A=[aij]의 성분 aij의 여인자를 Aij라 할 때, 행렬 [Aij]T를 A의 수반행렬(adjoint matrix)이라 하고, adj A 로 나타낸다. 즉, ex2> http://en.wikipedia.org/wiki/Adjugate 2 × 2 generic matrix The adjugate of the 2 × 2 matrix is . [edit] 3 × 3 generic matrix Consider the matrix . Its adjugate is the transpose of the cofactor matrix So that we have where . Note that the adjugate is the transpose.. 더보기 Determinant (ex) det(A) , Sarrus, Laplace's formula and the adjugate matrix determinant is written and has the value . Sarrus 방법 http://matrix.skku.ac.kr/sglee/linear/ocu/20301.html Laplace's formula and the adjugate matrix Laplace's formula expresses the determinant of a matrix in terms of its minors. The minor Mi,j is defined to be the determinant of the (n−1)×(n−1)-matrix that results from A by removing the i-th row and the j-th column. The expression (−1)i+jMi,j is .. 더보기 homogemeous metrix, nonhomogemeous metrix b1,b2, ... , bm 이 모두 0 이면 homogeneous 그렇지 않으면 nonhomogeneous homogeneous metrix 의 표현 Ax = O 더보기 inverse metrix, invertible, noninvertible AB = In = BA B는 A 의 inverse metrix A 의 inverse metrix 가 존재하면 A 를 invertible 하다고 한다. A 의 inverse metrix 가 존재하지 않으면 A 를 noninvertible 하다고 한다. Inverse of 3 x 3 matrices Example 1: Find the inverse of Solution: Step 1: Adjoin the identity matrix to the right side of A: Step 2: Apply row operations to this matrix until the left side is reduced to I. The computations are: Step 3: Conclusion: The inver.. 더보기 row echelon form (ref), reduced row echelon form (rref) row echelon form (ref) reduced row echelon form (rref) 더보기 transpose metrix, symmetric metrix 행렬 A=[aij ]m×n 에 대하여 A의 전치행렬(transpose of A)을 AT로 나타내 고 다음과 같이 정의한다. 정사각행렬 A가 AT = A 를 만족하면 A를 대칭행렬(symmetric matrix)이라 하고, AT =-A 를 만족하면 반대칭행렬(skew symmetric matrix)이라고 한다. 더보기 이전 1 2 다음
