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페이스북 트위터 카카오톡 네이버밴드 링크복사

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자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
강의학기

2014년 1학기

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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.

수강안내 및 수강신청
※ 수강확인증 발급을 위해서는 수강신청이 필요합니다

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)