## 주메뉴

### 선형대수

• 건국대학교
• 이향원
• 주제분류
자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
• 강의학기
2014년 1학기
• 조회수
34,867
•
This course introduces elementary linear algebra. In particular, we will study vectors, matrices, determinants, linear equations, vector spaces and subspaces, eigenvalues/eigenvectors. As we move toward the end of the semester, there will be some projects that require you to apply the materials discussed in the lectures in order to solve the real-world problems. To do this, we will probably have one class for learning MATLAB which is a very useful language for calculations in linear algebra.
Introduction, Vectors and matrices

#### 차시별 강의

 1. Introduction, Vectors and matrices Administrative annoucements - Vectors and basic operations - Matrices and basic operations - Special matrices Introduction, Vectors and matrices Administrative annoucements - Vectors and basic operations - Matrices and basic operations - Special matrices 2. Linear equations - Matrix-vector representation of linear equations - Elimination methods Linear equations - Matrix-vector representation of linear equations - Elimination methods 3. Factorization Elimination and factorization - Symetric matrices and factorization Factorization Elimination and factorization - Symetric matrices and factorization 4. Vector spaces and subspaces Spaces of vectors - Column spaces of a matrix - Null space of a matrix Vector spaces and subspaces Spaces of vectors - Column spaces of a matrix - Null space of a matrix 5. Rank of a matrix Rank of a matrix - Row reduced form - Solution to Ax=b Rank of a matrix Rank of a matrix - Row reduced form - Solution to Ax=b 6. Independence, basis and dimension Linear independence of vectors - Basis for a space - Dimension of a space - Dimensions of the four fundamental subspaces Independence, basis and dimension Linear independence of vectors - Basis for a space - Dimension of a space - Dimensions of the four fundamental subspaces Independence, basis and dimension Linear independence of vectors - Basis for a space - Dimension of a space - Dimensions of the four fundamental subspaces 7. Orthogonality Orthogonality of the four subspaces Orthogonality Orthogonality of the four subspaces Orthogonality Orthogonality of the four subspaces Orthogonality Orthogonality of the four subspaces 8. Applications Least squares approximations - Orthogonal bases and Gram-Schmidt process Applications Least squares approximations - Orthogonal bases and Gram-Schmidt process 9. Determinants Properties of determinants - Permutations and cofactors 10. Cramer's rule Solution to Ax=b - Formula for inverse matrix Cramer's rule Solution to Ax=b - Formula for inverse matrix 11. Eigenvalues Definition of eigenvalues and eigenvectors - Properties of eigenvalues and eigenvectors Eigenvalues Definition of eigenvalues and eigenvectors - Properties of eigenvalues and eigenvectors Eigenvalues Definition of eigenvalues and eigenvectors - Properties of eigenvalues and eigenvectors 12. Diagonalization Diagonalizing a matrix - Convergence of a matrix series and eigenvalues - Nondiagonalizable matrices Diagonalization Diagonalizing a matrix - Convergence of a matrix series and eigenvalues - Nondiagonalizable matrices 13. Symmetric matrices Eigenvalues and eigenvectors of symmetric matrices - Positive definite matrices 14. Similar matrices Definition of similar matrices - Jordan form - Singular value decomposition (SVD) Similar matrices Definition of similar matrices - Jordan form - Singular value decomposition (SVD) Similar matrices Definition of similar matrices - Jordan form - Singular value decomposition (SVD)

#### 사용자 의견

강의 평가를 위해서는 로그인 해주세요.
운영자2016-06-20 16:00
KOCW운영팀입니다. 강의교재는 Introduction to Linear Algebra, Gilbert Strang, Wellesley-Cambridge 입니다.
운영자2016-06-16 09:58
KOCW운영팀입니다. 건국대학교로 강의교재에 대해 문의하였습니다. 답변이 오는대로 안내 드리도록 하겠습니다.
ph1601 2016-06-15 14:05
강의교재는 뭘쓰나요?

#### 이용방법

• 비디오 강의 이용시 필요한 프로그램 [바로가기]

※ 강의별로 교수님의 사정에 따라 전체 차시 중 일부 차시만 공개되는 경우가 있으니 양해 부탁드립니다.