Nguồn ngoài
Interactive Linear Algebra
The name of the textbook highlights an important theme: the synthesis between algebra and geometry. It will be very important to us to understand systems of linear equations both algebraically (writing equations for their solutions) and geometrically (drawing pictures and visualizing).
- Tác giả
- Dan Margalit & Joseph Rabinoff
- Nhà xuất bản
- Georgia Institute of Technology
- Nguồn
- LibreTexts
- Giấy phép
- GNU FDL
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 43 mục
- 01: Systems of Linear Equations- Algebra
- 1.01: Systems of Linear Equations
- 1.02: Row Reduction
- 1.03: Parametric Form
- 02: Systems of Linear Equations- Geometry
- 2.01: Vectors
- 2.02: Vector Equations and Spans
- 2.03: Matrix Equations
- 2.04: Solution Sets
- 2.05: Linear Independence
- 2.06: Subspaces
- 2.07: Basis and Dimension
- 2.8: Bases as Coordinate Systems
- 2.08: The Rank Theorem
- 03: Linear Transformations and Matrix Algebra
- 3.00: Prelude to Linear Transformations and Matrix Algebra
- 3.01: Matrix Transformations
- 3.02: One-to-one and Onto Transformations
- 3.03: Linear Transformations
- 3.04: Matrix Multiplication
- 3.05: Matrix Inverses
- 3.06: The Invertible Matrix Theorem
- 04: Determinants
- 4.01: Determinants- Definition
- 4.02: Cofactor Expansions
- 4.03: Determinants and Volumes
- 05: Eigenvalues and Eigenvectors
- 5.01: Eigenvalues and Eigenvectors
- 5.02: The Characteristic Polynomial
- 5.03: Diagonalization
- 5.3: Similarity
- 5.04: Complex Eigenvalues
- 5.05: Stochastic Matrices
- 06: Orthogonality
- 6.01: Dot Products and Orthogonality
- 6.02: Orthogonal Complements
- 6.03: Orthogonal Projection
- 6.04: The Method of Least Squares
- 6.5: The Method of Least Squares
- 07: Appendix
- 7.01: A - Complex Numbers
- 7.02: B - Notation
- 7.03: C - Hints and Solutions to Selected Exercises