Solution manual for Linear Algebra A Modern Introduction 4th Edition by David Poole- Ebook PDF Instant Download/Delivery:9781285463247,1285463242
Full dowload Linear Algebra A Modern Introduction 4th Edition after payment
Product details:
ISBN 10: 1285463242
ISBN 13:9781285463247
Author: David Poole
David Poole’s innovative LINEAR ALGEBRA: A MODERN INTRODUCTION, 4e emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning. Theoretical, computational, and applied topics are presented in a flexible yet integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems.
Linear Algebra A Modern Introduction 4th Table of contents:
1. Vectors
1.0. Introduction: The Racetrack Game
1.1. The Geometry and Algebra of Vectors
Vectors in the Plane
New Vectors from Old
Vectors in ℝ 3
Vectors in ℝ n
Linear Combinations and Coordinates
Binary Vectors and Modular Arithmetic
Exercises 1.1.
1.2. Length and Angle: The Dot Product
The Dot Product
Length
Distance
Angles
Orthogonal Vectors
Projections
Exercises 1.2.
Exploration
1.3. Lines and Planes
Lines in ℝ 2 and ℝ 3
Planes in ℝ 3
Exercises 1.3.
Exploration
1.4. Applications
Force Vectors
Exercises 1.4.
Key Definitions and Concepts
Review Questions
2. Systems of Linear Equations
2.0. Introduction: Triviality
2.1. Introduction to Systems of Linear Equations
Solving a System of Linear Equations
Exercises 2.1.
2.2. Direct Methods for Solving Linear Systems
Matrices and Echelon Form
Elementary Row Operations
Gaussian Elimination
Gauss-Jordan Elimination
Homogeneous Systems
Linear Systems over ℤ p
Exercises 2.2.
Explorations
2.3. Spanning Sets and Linear Independence
Spanning Sets of Vectors
Linear Independence
Exercises 2.3.
2.4. Applications
Allocation of Resources
Balancing Chemical Equations
Network Analysis
Electrical Networks
Linear Economic Models
Finite Linear Games
Exercises 2.4.
Vignette
2.5. Iterative Methods for Solving Linear Systems
Exercises 2.5.
Key Definitions and Concepts
Review Questions
3. Matrices
3.0. Introduction: Matrices in Action
3.1. Matrix Operations
Matrix Addition and Scalar Multiplication
Matrix Multiplication
Partitioned Matrices
Matrix Powers
The Transpose of a Matrix
Exercises 3.1.
3.2. Matrix Algebra
Properties of Addition and Scalar Multiplication
Properties of Matrix Multiplication
Properties of the Transpose
Exercises 3.2.
3.3. The Inverse of a Matrix
Properties of Invertible Matrices
Elementary Matrices
The Fundamental Theorem of Invertible Matrices
The Gauss-Jordan Method for Computing the Inverse
Exercises 3.3.
3.4. The LU Factorization
An Easy Way to Find LU Factorizations
The P T LU Factorization
Computational Considerations
Exercises 3.4.
3.5. Subspaces, Basis, Dimension, and Rank
Subspaces Associated with Matrices
Basis
Dimension and Rank
Coordinates
Exercises 3.5.
3.6. Introduction to Linear Transformations
Linear Transformations
New Linear Transformations from Old
Inverses of Linear Transformations
Associativity
Exercises 3.6.
Vignette
3.7. Applications
Markov Chains
Linear Economic Models
Population Growth
Graphs and Digraphs
Exercises 3.7.
Key Definitions and Concepts
Review Questions
4. Eigenvalues and Eigenvectors
4.0. Introduction: A Dynamical System on Graphs
4.1. Introduction to Eigenvalues and Eigenvectors
Exercises 4.1.
4.2. Determinants
Determinants of n × n Matrices
Properties of Determinants
Determinants of Elementary Matrices
Determinants and Matrix Operations
Cramer’s Rule and the Adjoint
Proof of the Laplace Expansion Theorem
A Brief History of Determinants
Exercises 4.2.
Vignette
Exploration
4.3. Eigenvalues and Eigenvectors of n × n Matrices
Exercises 4.3.
4.4. Similarity and Diagonalization
Similar Matrices
Diagonalization
Exercises 4.4.
4.5. Iterative Methods for Computing Eigenvalues
The Power Method
The Shifted Power Method and the Inverse Power Method
The Shifted Inverse Power Method
Gerschgorin’s Theorem
Exercises 4.5.
4.6. Applications and the Perron-Frobenius Theorem
Markov Chains
Population Growth
The Perron-Frobenius Theorem
Linear Recurrence Relations
Systems of Linear Differential Equations
Discrete Linear Dynamical Systems
Vignette
Exercises 4.6.
Key Definitions and Concepts
Review Questions
5. Orthogonality
5.0. Introduction: Shadows on a Wall
5.1. Orthogonality in ℝ n
Orthogonal and Orthonormal Sets of Vectors
Orthogonal Matrices
Exercises 5.1.
5.2. Orthogonal Complements and Orthogonal Projections
Orthogonal Complements
Orthogonal Projections
Exercises 5.2.
5.3. The Gram-Schmidt Process and the QR Factorization
The Gram-Schmidt Process
The QR Factorization
Exercises 5.3.
Explorations
5.4. Orthogonal Diagonalization of Symmetric Matrices
Exercises 5.4.
5.5. Applications
Quadratic Forms
Graphing Quadratic Equations
Exercises 5.5.
Key Definitions and Concepts
Review Questions
6. Vector Spaces
6.0. Introduction: Fibonacci in (Vector) Space
6.1. Vector Spaces and Subspaces
Subspaces
Spanning Sets
Exercises 6.1.
6.2. Linear Independence, Basis, and Dimension
Linear Independence
Bases
Coordinates
Dimension
Exercises 6.2.
Exploration
6.3. Change of Basis
Change-of-Basis Matrices
The Gauss-Jordan Method for Computing a Change-of-Basis Matrix
Exercises 6.3.
6.4. Linear Transformations
Properties of Linear Transformations
Composition of Linear Transformations
Inverses of Linear Transformations
Exercises 6.4.
6.5. The Kernel and Range of a Linear Transformation
One-to-One and Onto Linear Transformations
Isomorphisms of Vector Spaces
Exercises 6.5.
6.6. The Matrix of a Linear Transformation
Matrices of Composite and Inverse Linear Transformations
Change of Basis and Similarity
Exercises 6.6.
Exploration
6.7. Applications
Homogeneous Linear Differential Equations
Exercises 6.7.
Key Definitions and Concepts
Review Questions
7. Distance and Approximation
7.0. Introduction: Taxicab Geometry
7.1. Inner Product Spaces
Properties of Inner Products
Length, Distance, and Orthogonality
Orthogonal Projections and the Gram-Schmidt Process
The Cauchy-Schwarz and Triangle Inequalities
Exercises 7.1.
Explorations
7.2. Norms and Distance Functions
Distance Functions
Matrix Norms
The Condition Number of a Matrix
The Convergence of Iterative Methods
Exercises 7.2.
7.3. Least Squares Approximation
The Best Approximation Theorem
Least Squares Approximation
Solution of the Least Squares Problem
Least Squares via the QR Factorization
Orthogonal Projection Revisited
The Pseudoinverse of a Matrix
Exercises 7.3.
7.4. The Singular Value Decomposition
The Singular Values of a Matrix
The Singular Value Decomposition
Applications of the SVD
Vignette
Exercises 7.4.
7.5. Applications
Approximation of Functions
Exercises 7.5.
Key Definitions and Concepts
Review Questions
8. Codes
8.1. Code Vectors
Exercises 8.1.
Vignette
8.2. Error-Correcting Codes
Exercises 8.2.
8.3. Dual Codes
Exercises 8.3.
8.4. Linear Codes
Exercises 8.4.
8.5. The Minimum Distance of a Code
Exercises 8.5.
People also search for Linear Algebra A Modern Introduction 4th:
linear algebra a modern introduction 4th edition answer key
d. poole linear algebra a modern introduction 4th edition
linear algebra a modern introduction answers
linear algebra a modern introduction 4th edition chegg
linear algebra a modern introduction 4th edition by david poole
Reviews
There are no reviews yet.