Math 26: Introduction to Linear Algebra

This textbook covers a standard first linear algebra course. Studies include vectors; vector spaces and subspaces; matrices; systems of linear equations; dimension; determinants; eigenvalues and eigenvectors; and linear transformations and their applications.

Mathematics

Tác giả: Kenn Huber
Nhà xuất bản: Irvine Valley College
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 107 mục

01: Systems of Linear Equations
1.01: Systems of Linear Equations
1.1.01: Lines Planes and Space
1.1.02: Parametric Descriptions
1.1.03: Practice Set
1.02: Row Reduction
1.2.01: Elimination and Augmented Matrices
1.2.02: Echelon Forms
1.2.03: Free Variables
1.2.04: Practice Set
1.03: Vectors
1.3.01: Vector Algebra and Geometry
1.3.02: Vector Equations and Spans
1.3.03: Practice Set
1.04: Matrix Equations
1.4.01: Matrix Equations Spans and Consistency
1.4.02: Solutions to Matrix Equations
1.4.03: Practice Set
1.05: Linear Independence
1.5.01: Defining Linear Independence
1.5.02: Understanding Linear Independence
1.5.03: Practice Set
1.06: Subspaces
1.6.01: Defining Subspaces
1.6.02: Common Subspaces
1.6.03: Practice Set
1.07: Basis and Dimension
1.7.01: Defining Basis
1.7.02: Finding a Basis of a Subspace
1.7.03: Rank and Nullity
1.7.04: Practice Set
02: Linear Transformations and Matrix Algebra
2.01: Matrix Transformations
2.1.01: Matrices as Functions
2.1.02: Matrix Transformations
2.1.03: Practice Set
2.02: Linear Transformations
2.2.01: Linear Transformations
2.2.02: Matrix Representations
2.2.03: Practice Set
2.03: Matrix Algebra
2.3.01: Sums of Transformations and Matrices
2.3.02: Transformation Composition and Matrix Multiplication
2.3.03: Matrix Inverses
2.3.04: Practice Set
2.04: Invertibility
2.4.01: Invertibility of Linear Transformations
2.4.02: Invertibility of Matrices
2.4.03: Practice Set
2.05: Determinants- Definition
2.5.01: Definition of Determinant
2.5.02: Properties of the Determinant
2.5.03: Practice Set
2.06: Cofactor Expansions
2.6.01: Cofactor Expansion
2.6.02: Cramer's Rule and Adjugates
2.6.03: Practice Set
2.07: Determinants and Volumes
2.7.01: Determinants for Area and Volume
2.7.02: Practice Set
03: Vector Geometry
3.01: Change of Basis
3.1.01: Coordinatization
3.1.02: Similar Matrices
3.1.03: Practice Set
3.02: Eigenvalues and Eigenvectors
3.2.01: Eigenvalues and Eigenvectors Definitions
3.2.02: Eigenspaces
3.2.03: Characteristic Polynomial
3.2.04: Practice Set
3.03: Diagonalization and Geometry of Eigenvalues
3.3.01: Diagonalization
3.3.02: Geometry of Diagonalizable Matrices
3.3.03: Practice Set
3.04: Complex Eigenvalues
3.4.01: Complex Eigenvalues and Eigenvectors
3.4.02: Geometry of Matrices with Complex Eigenvalues
3.4.03: Practice Set
3.05: Dot Products and Orthogonal Complements
3.5.01: Dot Products and Orthogonality
3.5.02: Orthogonal Complements
3.5.03: Practice Set
3.06: Orthogonal Projection and Least Squares
3.6.01: Orthogonal Decomposition
3.6.02: Least Squares Solutions
3.6.03: Practice Set
3.07: Orthogonal Sets
3.7.01: Orthogonal Sets and Projection
3.7.02: Gram-Schmidt Process
3.7.03: Practice Set
04: Vector Spaces
4.01: General Vector Spaces and Subspaces
4.1.01: General Vector Spaces
4.1.02: Calculations in Vector Spaces
4.1.03: Practice Set
4.02: Linear Transformations in General Vector Spaces
4.2.01: Linear Transformations
4.2.02: Coordinatization
4.2.03: Practice Set
4.03: Examples and Applications
4.3.01: Differential Equations
4.3.02: Famous Transformations
4.3.03: Inner Product Spaces
4.3.04: Markov Chains
4.3.05: Page Rank
4.3.06: Practice Set
4.3.06: Quadratic Forms