第一週

• 1.1 Introduction to Systems of Linear Equations
  1.2 Gaussian Elimination

• 1.3 Applications of Systems of Linear Equations
  2.1 Operations with Matrices
  2.2 Properties of Matrix Operations

• 2.3 The Inverse of a Matrix
  2.4 Elementary Matrices
  2.5 Applications of Matrix Operations

• 3.1 The Determinant of a Matrix ;
  3.2 Evaluation of a Determinant Using Elementary Operations

• 3.3 Properties of Determinants
  3.5 Applications of Determinants;
  4.1 Vectors in Rn

• Prelim Examination I (Ch1-Ch3) (Exact date and time will be announced.)
  4.2 Vector Spaces;

• 4.3 Subspaces of Vector Spaces;
  4.4 Spanning Sets and Linear Independence

• 4.4 Spanning Sets and Linear Independence
  4.5 Basis and Dimension

• 4.5 Basis and Dimension
  4.6 Rank of a Matrix

• 4.7 Coordinates and Change of Basis
  5.1 Length and Dot Product

• 5.2 Inner Product Spaces
  5.3 Orthogonal Basis

• 5.3 Orthogonal Basis;
  5.4 Least Square Analysis

• Prelim Examination II ( Ch4-Ch5) (Exact date and time will be announced.)
  6.1 Introduction to Linear Transformation

• 6.1 Introduction to Linear Transformation;
  6.2 Kernel and Range

• 6.3 Matrices for Linear Transformations;
  6.4 Transition Matrices and Similarity

• 7.1 Eigenvalues and Eigenvectors;
  7.2 Diagonalization　

• 7.2 Diagonalization;
  7.3 Symmetrical Matrices and Orthogonal Diagonalization

• Final Examination (Ch6-Ch7) (Exact date and time will be announced)