Elementary Linear Algebra, 8th Edition

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. This new edition is now fully supported by two optional strong digital learning solutions, Enhanced WebAssign and MindTap Math, and the companion website LarsonLinearAlgebra.com offers free access to multiple tools and resources to supplement students’ learning.

Table of Contents

1. SYSTEMS OF LINEAR EQUATIONS.
Introduction to Systems of Equations. Gaussian Elimination and Gauss-Jordan Elimination. Applications of Systems of Linear Equations.

2. MATRICES.
Operations with Matrices. Properties of Matrix Operations. The Inverse of a Matrix. Elementary Matrices. Markov Chains. Applications of Matrix Operations.

3. DETERMINANTS.
The Determinant of a Matrix. Evaluation of a Determinant Using Elementary Operations. Properties of Determinants. Applications of Determinants.

4. VECTOR SPACES.
Vectors in Rn. Vector Spaces. Subspaces of Vector Spaces. Spanning Sets and Linear Independence. Basis and Dimension. Rank of a Matrix and Systems of Linear Equations. Coordinates and Change of Basis. Applications of Vector Spaces.

5. INNER PRODUCT SPACES.
Length and Dot Product in Rn. Inner Product Spaces. Orthogonal Bases: Gram-Schmidt Process. Mathematical Models and Least Squares Analysis. Applications of Inner Product Spaces.

6. LINEAR TRANSFORMATIONS.
Introduction to Linear Transformations. The Kernel and Range of a Linear Transformation. Matrices for Linear Transformations. Transition Matrices and Similarity. Applications of Linear Transformations.

7. EIGENVALUES AND EIGENVECTORS.
Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices and Orthogonal Diagonalization. Applications of Eigenvalues and Eigenvectors.

8. COMPLEX VECTOR SPACES (online).
Complex Numbers. Conjugates and Division of Complex Numbers. Polar Form and Demoivre’s Theorem. Complex Vector Spaces and Inner Products. Unitary and Hermitian Spaces.

9. LINEAR PROGRAMMING (online).
Systems of Linear Inequalities. Linear Programming Involving Two Variables. The Simplex Method: Maximization. The Simplex Method: Minimization. The Simplex Method: Mixed Constraints.

10. NUMERICAL METHODS (online).
Gaussian Elimination with Partial Pivoting. Iterative Methods for Solving Linear Systems. Power Method for Approximating Eigenvalues. Applications of Numerical Methods.

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