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

 
這份閱讀導覽按照我為《教學光碟》撰寫的《線性代數講義本》編排,涵蓋基礎線性代數的七大主題:線性方程與矩陣代數、向量空間、線性變換、正交 (內積空間)、行列式、特徵分析和二次型。小節標題代表重要的線性代數辭條,各小節間環環相扣,因此存在某種層次關係。為便利讀者參照查閱,各小節編列與主題旨趣相關的文章連結,其中凡標記 * 者,代表此文內容較為艱深冷僻,省略該文並不會妨礙理解核心觀念。除此之外,讀者亦可利用本網誌的「搜尋」與「標籤」功能查找更多的相關文件。

 
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

 
Chapter 7 Quadratic Forms

7-1 Symmetric Matrices
7-2 Introduction to Quadratic Forms
7-3 Positive Definite Matrices
7-4 Singular Values
7-5 Singular Value Decomposition
Applications

發表迴響

在下方填入你的資料或按右方圖示以社群網站登入:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / 變更 )

Twitter picture

You are commenting using your Twitter account. Log Out / 變更 )

Facebook照片

You are commenting using your Facebook account. Log Out / 變更 )

Google+ photo

You are commenting using your Google+ account. Log Out / 變更 )

連結到 %s