Nguồn ngoài
Linear Algebra
Linear algebra is the study of vectors and linear transformations. This text is suitable for a sophomore level linear algebra course taught in about twenty-five lectures. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. Our goal in writing it was to produce students who can perform computations with linear systems and also understand the concepts behind these computations.
- Tác giả
- David Cherney, Tom Denton, & Andrew Waldron
- Nhà xuất bản
- University of California, Davis
- Nguồn
- LibreTexts
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 103 mục
- 01: What is Linear Algebra
- 1.01: What Are Vectors
- 1.02: What Are Linear Functions
- 1.03: What is a Matrix
- 1.04: Review Problems
- 02: Systems of Linear Equations
- 2.01: Gaussian Elimination
- 2.02: Review Problems
- 2.03: Elementary Row Operations
- 2.04: Review Problems
- 2.05: Solution Sets for Systems of Linear Equations
- 2.06: Review Problems
- 03: The Simplex Method
- 3.01: Pablo's Problem
- 3.02: Graphical Solutions
- 3.03: Dantzig's Algorithm
- 3.04: Pablo Meets Dantzig
- 3.05: Review Problems
- 04: Vectors in Space n-Vectors
- 4.01: Addition and Scalar Multiplication in (mathbbRn)
- 4.02: Hyperplanes
- 4.03: Directions and Magnitudes
- 4.04: Vectors Lists and Functions- (mathbbRS)
- 4.05: Review Problems
- 05: Vector Spaces
- 5.01: Examples of Vector Spaces
- 5.02: Other Fields
- 5.03: Review Problems
- 06: Linear Transformations
- 6.01: The Consequence of Linearity
- 6.02: Linear Functions on Hyperplanes
- 6.03: Linear Differential Operators
- 6.04: Bases (Take 1)
- 6.05: Review Problems
- 07: Matrices
- 7.01: Linear Transformations and Matrices
- 7.02: Review Problems
- 7.03: Properties of Matrices
- 7.04: Review Problems
- 7.05: Inverse Matrix
- 7.06: Review Problems
- 7.07: LU Redux
- 7.08: Review Problems
- 08: Determinants
- 8.01: The Determinant Formula
- 8.02: Elementary Matrices and Determinants
- 8.03: Review Problems
- 8.04: Properties of the Determinant
- 8.05: Review Problems
- 09: Subspaces and Spanning Sets
- 9.01: Subspaces
- 9.02: Building Subspaces
- 9.03: Review Problems
- 10: Linear Independence
- 10.01: Showing Linear Dependence
- 10.02: Showing Linear Independence
- 10.03: From Dependent Independent
- 10.04: Review Problems
- 11: Basis and Dimension
- 11.01: Bases in (Ren)
- 11.02: Matrix of a Linear Transformation (Redux)
- 11.03: Review Problems
- 12: Eigenvalues and Eigenvectors
- 12.01: Invariant Directions
- 12.02: The Eigenvalue-Eigenvector Equation
- 12.03: Eigenspaces
- 12.04: Review Problems
- 13: Diagonalization
- 13.01: Diagonalization
- 13.02: Change of Basis
- 13.03: Changing to a Basis of Eigenvectors
- 13.04: Review Problems
- 14: Orthonormal Bases and Complements
- 14.01: Properties of the Standard Basis
- 14.02: Orthogonal and Orthonormal Bases
- 14.03: Relating Orthonormal Bases
- 14.04: Gram-Schmidt and Orthogonal Complements
- 14.05: QR Decomposition
- 14.06: Orthogonal Complements
- 14.07: Review Problems
- 15: Diagonalizing Symmetric Matrices
- 15.01: Review Problems
- 16: Kernel Range Nullity Rank
- 16.01: Summary
- 16.02: Review Problems
- 17: Least Squares and Singular Values
- 17.01: Singular Value Decomposition
- 17.02: Review Problems
- 18: Symbols Fields Sample Exams Online Resources Movie Scripts
- 18.01: List of Symbols
- 18.02: Fields
- 18.03: Online Resources
- 18.04: Sample First Midterm
- 18.05: Sample Second Midterm
- 18.06: Sample Final Exam
- 18.07: Movie Scripts 1-2
- 18.08: Movie Scripts 3-4
- 18.09: Movie Scripts 5-6
- 18.10: Movie Scripts 7-8
- 18.11: Movie Scripts 9-10
- 18.12: Movie Scripts 11-12
- 18.13: Movie Scripts 13-14
- 18.14: Movie Scripts 15-16