PowerPoint Presentation for Linear Algebra and Its Applications, Global Edition

1. Linear Equations in LinearAlgebra

Introductory Example: LinearModels in Economics and Engineering

1.1 Systems of Linear Equations

1.2 Row Reduction and EchelonForms

1.3 Vector Equations

1.4 The Matrix Equation Ax= b

1.5 Solution Sets of LinearSystems

1.6 Applications of Linear Systems

1.7 Linear Independence

1.8 Introduction to LinearTransformations

1.9 The Matrix of a LinearTransformation

1.10 Linear Models in Business,Science, and Engineering

Projects

Supplementary Exercises

 

2. Matrix Algebra

Introductory Example: ComputerModels in Aircraft Design

2.1 Matrix Operations

2.2 The Inverse of a Matrix

2.3 Characterizations ofInvertible Matrices

2.4 Partitioned Matrices

2.5 Matrix Factorizations

2.6 The Leontief Input—OutputModel

2.7 Applications to ComputerGraphics

2.8 Subspaces of ℝn

2.9 Dimension and Rank

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Supplementary Exercises

 

3. Determinants

Introductory Example: Random Pathsand Distortion

3.1 Introduction to Determinants

3.2 Properties of Determinants

3.3 Cramer’s Rule, Volume, andLinear Transformations

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Supplementary Exercises

 

4. Vector Spaces

Introductory Example: Space Flightand Control Systems

4.1 Vector Spaces and Subspaces

4.2 Null Spaces, Column Spaces,and Linear Transformations

4.3 Linearly Independent Sets;Bases

4.4 Coordinate Systems

4.5 The Dimension of a VectorSpace

4.6 Change of Basis

4.7 Digital Signal Processing

4.8 Applications to DifferenceEquations

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Supplementary Exercises

 

5. Eigenvalues and Eigenvectors

Introductory Example: DynamicalSystems and Spotted Owls

5.1 Eigenvectors and Eigenvalues

5.2 The Characteristic Equation

5.3 Diagonalization

5.4 Eigenvectors and LinearTransformations

5.5 Complex Eigenvalues

5.6 Discrete Dynamical Systems

5.7 Applications to DifferentialEquations

5.8 Iterative Estimates forEigenvalues

5.9 Markov Chains

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Supplementary Exercises

 

6. Orthogonality and Least Squares

Introductory Example: The NorthAmerican Datum and GPS Navigation

6.1 Inner Product, Length, andOrthogonality

6.2 Orthogonal Sets

6.3 Orthogonal Projections

6.4 The Gram—Schmidt Process

6.5 Least-Squares Problems

6.6 Machine Learning and LinearModels

6.7 Inner Product Spaces

6.8 Applications of Inner ProductSpaces

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Supplementary Exercises

 

7. Symmetric Matrices andQuadratic Forms

Introductory Example: MultichannelImage Processing

7.1 Diagonalization of SymmetricMatrices

7.2 Quadratic Forms

7.3 Constrained Optimization

7.4 The Singular ValueDecomposition

7.5 Applications to ImageProcessing and Statistics

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Supplementary Exercises

 

8. The Geometry of Vector Spaces

Introductory Example: The PlatonicSolids

8.1 Affine Combinations

8.2 Affine Independence

8.3 Convex Combinations

8.4 Hyperplanes

8.5 Polytopes

8.6 Curves and Surfaces

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Supplementary Exercises

 

9. Optimization

Introductory Example: The BerlinAirlift

9.1 Matrix Games

9.2 Linear Programming–GeometricMethod

9.3 Linear Programming–SimplexMethod

9.4 Duality

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Supplementary Exercises

 

10. Finite-State Markov Chains(Online Only)

Introductory Example: GooglingMarkov Chains

10.1 Introduction and Examples

10.2 The Steady-State Vector andGoogle's PageRank

10.3 Communication Classes

10.4 Classification of States andPeriodicity

10.5 The Fundamental Matrix

10.6 Markov Chains and BaseballStatistics

 

Appendices

A. Uniqueness of the ReducedEchelon Form

B. Complex Numbers