# 線性代數教學光碟延伸閱讀

Technical skill is mastery of complexity while creativity is mastery of simplicity.
― E. Christopher Zeeman

Chapter 1 Linear Equations and Matrix Algebra

1-1 System of Linear Equations
1-2 Elimination
1-3 Elimination Using Matrix Multiplications
1-4 Matrix Algebra
1-5 Inverse Matrices
1-6 Finding the Inverse
1-7 LU Factorization
1-8 Transposes
1-9 Block Matrices
Applications

Chapter 2 Vector Spaces

2-1 Vector Spaces and Subspaces
2-2 Column Space and Nullspace
2-3 Reduced Row Echelon Form
2-4 General Solutions to Ax=b
2-5 Independence, Basis and Dimension
2-6 Four Fundamental Subspaces
2-7 Existence and Uniqueness of Inverses
Applications

Chapter 3 Linear Transformations

3-1 Introduction to Linear Transformations
3-2 Language of Transformations
3-3 Coordinate Systems and General Vector Spaces
3-4 Matrices of Linear Transformations
3-5 Change of Basis

Chapter 4 Orthogonality

4-1 Orthogonal Vectors and Orthogonal Subspaces
4-2 Projections
4-3 Least Squares Approximations
4-4 Orthogonal Matrices
4-5 Gram-Schmidt Process
Applications

Chapter 5 Determinants

5-1 Properties of Determinants
5-2 Formulas for Determinants
5-3 Applications of Determinants
Applications

Chapter 6 Eigenanalysis

6-1 Eigenvalues and Eigenvectors
6-2 Properties of Eigenvalues and Eigenvectors
6-3 Diagonalization
6-4 Difference Equations
6-5 Differential Equations
6-6 Complex Eigenvalues
6-7 Similar Matrices
Applications