Elementary Linear Algebra 8th Edition by Ron Larson 9798214342214

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ISBN-13 : 9798214342214

Author : Ron Larson 

The cornerstone of ELEMENTARY LINEAR ALGEBRA is the author’s clear, careful, and concise presentation of material–written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. Featuring a new design that highlights the relevance of the mathematics and improves readability for students, the Eighth Edition also incorporates conceptual Capstone exercises that reinforce multiple concepts in each section. Data and applications reflect current statistics and examples to engage students and demonstrate the link between theory and practice.

 

Elementary Linear Algebra 8th Table of contents:

1. Systems of Linear Equations
1.1. Introduction to Systems of Linear Equations
Linear Equations in n Variables
Solutions and Solution Sets
Systems of Linear Equations
Solving a System of Linear Equations
1.1. Exercises
1.2. Gaussian Elimination and Gauss-Jordan Elimination
Matrices
Elementary Row Operations
Gauss-Jordan Elimination
Homogeneous Systems of Linear Equations
1.2. Exercises
1.3. Applications of Systems of Linear Equations
Polynomial Curve Fitting
Network Analysis
1.3. Exercises
1. Review Exercises
1. Projects
2. Matrices
2.1. Operations with Matrices
Equality of Matrices
Matrix Addition, Subtraction, and Scalar Multiplication
Matrix Multiplication
Systems of Linear Equations
Partitioned Matrices
2.1. Exercises
2.2. Properties of Matrix Operations
Algebra of Matrices
Properties of Matrix Multiplication
The Transpose of a Matrix
2.2. Exercises
2.3. The Inverse of a Matrix
Matrices and Their Inverses
Properties of Inverses
Systems of Equations
2.3. Exercises
2.4. Elementary Matrices
Elementary Matrices and Elementary Row Operations
The L U -Factorization
2.4. Exercises
2.5. Markov Chains
Stochastic Matrices and Markov Chains
Steady State Matrix of a Markov Chain
Absorbing Markov Chains
2.5. Exercises
2.6. More Applications of Matrix Operations
Cryptography
Leontief Input-Output Models
Least Squares Regression Analysis
2.6. Exercises
2. Review Exercises
2. Projects
3. Determinants
3.1. The Determinant of a Matrix
The Determinant of a 2 × 2 Matrix
Minors and Cofactors
The Determinant of a Square Matrix
Triangular Matrices
3.1. Exercises
3.2. Determinants and Elementary Operations
Determinants and Elementary Row Operations
Determinants and Elementary Column Operations
Matrices and Zero Determinants
3.2. Exercises
3.3. Properties of Determinants
Matrix Products and Scalar Multiples
Determinants and the Inverse of a Matrix
Determinants and the Transpose of a Matrix
3.3. Exercises
3.4. Applications of Determinants
The Adjoint of a Matrix
Cramer’s Rule
Area, Volume, and Equations of Lines and Planes
3.4. Exercises
3. Review Exercises
3. Projects
1-3. Cumulative Test
4. Vector Spaces
4.1. Vectors in R n
Vectors in the Plane
Vector Operations
Vectors in R n
Linear Combinations of Vectors
4.1. Exercises
4.2. Vector Spaces
Definition of a Vector Space
Sets that Are Not Vector Spaces
4.2. Exercises
4.3. Subspaces of Vector Spaces
Subspaces
Subspaces of R n
4.3. Exercises
4.4. Spanning Sets and Linear Independence
Linear Combinations of Vectors in a Vector Space
Spanning Sets
Linear Dependence and Linear Independence
4.4. Exercises
4.5. Basis and Dimension
Basis for a Vector Space
The Dimension of a Vector Space
4.5. Exercises
4.6. Rank of a Matrix and Systems of Linear Equations
Row Space, Column Space, and Rank of a Matrix
The Nullspace of a Matrix
Solutions of Systems of Linear Equations
4.6. Exercises
4.7. Coordinates and Change of Basis
Coordinate Representation in R n
Change of Basis in R n
Coordinate Representation in General n -Dimensional Spaces
4.7. Exercises
4.8. Applications of Vector Spaces
Linear Differential Equations (Calculus)
Conic Sections and Rotation
4.8. Exercises
4. Review Exercises
4. Projects
5. Inner Product Spaces
5.1. Length and Dot Product in R n
Vector Length and Unit Vectors
Distance Between Two Vectors in R n
Dot Product and the Angle Between Two Vectors
The Dot Product and Matrix Multiplication
5.1. Exercises
5.2. Inner Product Spaces
Inner Products
Orthogonal Projections in Inner Product Spaces
5.2. Exercises
5.3. Orthonormal Bases: Gram-Schmidt Process
Orthogonal and Orthonormal Sets
Gram-Schmidt Orthonormalization Process
5.3. Exercises
5.4. Mathematical Models and Least Squares Analysis
The Least Squares Problem
Orthogonal Subspaces
Fundamental Subspaces of a Matrix
Solving the Least Squares Problem
Mathematical Modeling
5.4. Exercises
5.5. Applications of Inner Product Spaces
The Cross Product of Two Vectors in R 3
Least Squares Approximations (Calculus)
Fourier Approximations (Calculus)
5.5. Exercises
5. Review Exercises
5. Projects
4 and 5 Cumulative Test
6. Linear Transformations
6.1. Introduction to Linear Transformations
Images and Preimages of Functions
Linear Transformations
6.1. Exercises
6.2. The Kernel and Range of a Linear Transformation
The Kernel of a Linear Transformation
The Range of a Linear Transformation
One-to-One and Onto Linear Transformations
Isomorphisms of Vector Spaces
6.2. Exercises
6.3. Matrices for Linear Transformations
The Standard Matrix for a Linear Transformation
Composition of Linear Transformations
Nonstandard Bases and General Vector Spaces
6.3. Exercises
6.4. Transition Matrices and Similarity
The Matrix for a Linear Transformation
Similar Matrices
6.4. Exercises
6.5. Applications of Linear Transformations
The Geometry of Linear Transformations in R 2
Rotation in R 3
6.5. Exercises
6. Review Exercises
6. Projects
7. Eigenvalues and Eigenvectors
7.1. Eigenvalues and Eigenvectors
The Eigenvalue Problem
Eigenspaces
Finding Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors of Linear Transformations
7.1. Exercises
7.2. Diagonalization
The Diagonalization Problem
Diagonalization and Linear Transformations
7.2. Exercises
7.3. Symmetric Matrices and Orthogonal Diagonalization
Symmetric Matrices
Orthogonal Matrices
Orthogonal Diagonalization
7.3. Exercises
7.4. Applications of Eigenvalues and Eigenvectors
Population Growth
Systems of Linear Differential Equations (Calculus)
Quadratic Forms
Constrained Optimization
7.4. Exercises
7. Review Exercises
7. Projects
6 and 7 Cumulative Test
8. Complex Vector Spaces
8.1. Complex Numbers
Complex Numbers
The Complex Plane
Addition, Subtraction, and Scalar Multiplication of Complex Numbers
Multiplication of Complex Numbers
Complex Matrices
8.1. Exercises
8.2. Conjugates and Division of Complex Numbers
Complex Conjugates
The Modulus of a Complex Number
Division of Complex Numbers
8.2. Exercises
8.3. Polar Form and DeMoivre’s Theorem
Polar Form of a Complex Number
DeMoivre’s Theorem
8.3. Exercises
8.4. Complex Vector Spaces and Inner Products
Complex Vector Spaces
Complex Inner Product Spaces
8.4. Exercises
8.5. Unitary and Hermitian Matrices
Conjugate Transpose of a Matrix
Unitary Matrices
Hermitian Matrices
8.5. Exercises
8. Review Exercises
8. Projects
9. Linear Programming
9.1. Systems of Linear Inequalities
Linear Inequalities and Their Graphs
Systems of Inequalities
9.1. Exercises
9.2. Linear Programming Involving Two Variables
Solving a Linear Programming Problem
Application
9.2. Exercises
9.3. The Simplex Method: Maximization
The Simplex Tableau
Pivoting
The Simplex Method
Applications
9.3. Exercises
9.4. The Simplex Method: Minimization
The Dual of a Minimization Problem
Solving a Minimization Problem
9.4. Exercises
9.5. The Simplex Method: Mixed Constraints
Mixed Constraints and Maximization
Mixed Constraints and Minimization
9.5. Exercises
9. Review Exercises
9. Project
10. Numerical Methods
10.1. Gaussian Elimination with Partial Pivoting
Stored Value and Rounding Error
Gaussian Elimination with Partial Pivoting
10.1. Exercises
10.2. Iterative Methods for Solving Linear Systems
The Jacobi Method
The Gauss-Seidel Method
Convergence and Divergence
10.2. Exercises
10.3. Power Method for Approximating Eigenvalues
Dominant Eigenvalues and Dominant Eigenvectors
The Power Method
10.3. Exercises
10.4. Applications of Numerical Methods
Applications of Gaussian Elimination with Partial Pivoting
Applications of the Gauss-Seidel Method
Applications of the Power Method
10.4. Exercises
10. Review
10. Projects

 

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