Linear Algebra and Its Applications 5th edition by David Lay, Steven Lay, Judi McDonald ISBN 032198238X 978-0321982384

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ISBN 10:  032198238X
ISBN 13: 978-0321982384
Author: David Lay, Steven Lay, Judi McDonald

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With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate. These concepts are fundamental to the study of linear algebra, so students’ understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete Rⁿ setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand.

Linear Algebra and Its Applications 5th Table of contents:

Chapter 1: Systems of Linear Equations

• 1.1: Linear Equations in Linear Algebra
• 1.2: Solution Sets of Linear Systems
• 1.3: Row Reduction and Echelon Forms
• 1.4: Vector Equations
• 1.5: The Matrix Equation Ax = b
• 1.6: Solving Systems of Linear Equations
• 1.7: Applications of Linear Systems
• Summary
• Applications
• Exercises

---

Chapter 2: Matrix Algebra

• 2.1: Matrix Operations
• 2.2: The Inverse of a Matrix
• 2.3: Characterizations of Invertible Matrices
• 2.4: Partitioned Matrices
• 2.5: Matrix Factorizations
• Summary
• Applications
• Exercises

---

Chapter 3: Determinants

• 3.1: Introduction to Determinants
• 3.2: Properties of Determinants
• 3.3: Cramer’s Rule
• 3.4: Volume and Linear Transformations
• Summary
• Applications
• Exercises

---

Chapter 4: Vector Spaces

• 4.1: Vector Spaces and Subspaces
• 4.2: Null Spaces, Column Spaces, and Linear Transformations
• 4.3: Linearly Independent Sets; Bases
• 4.4: The Dimension of a Vector Space
• 4.5: Coordinate Systems
• 4.6: The Four Subspaces of a Matrix
• Summary
• Applications
• Exercises

---

Chapter 5: Eigenvalues and Eigenvectors

• 5.1: Introduction to Eigenvalues and Eigenvectors
• 5.2: The Characteristic Equation
• 5.3: Diagonalization
• 5.4: Eigenvectors and Linear Transformations
• 5.5: Complex Eigenvalues
• Summary
• Applications
• Exercises

---

Chapter 6: Orthogonality

• 6.1: Inner Products, Lengths, and Orthogonality
• 6.2: Orthogonal Sets
• 6.3: Orthogonal Projections
• 6.4: Gram-Schmidt Process
• 6.5: Least Squares Problems
• 6.6: Applications of Orthogonality
• Summary
• Applications
• Exercises

---

Chapter 7: Diagonalization

• 7.1: Diagonalization of Matrices
• 7.2: Eigenvalues and Eigenvectors of Symmetric Matrices
• 7.3: Quadratic Forms
• 7.4: Applications of Diagonalization
• Summary
• Applications
• Exercises

---

Chapter 8: Vector Spaces of Functions

• 8.1: Vector Spaces of Polynomials
• 8.2: Function Spaces
• 8.3: Linear Transformations Between Function Spaces
• Summary
• Applications
• Exercises

---

Chapter 9: Linear Transformations

• 9.1: Introduction to Linear Transformations
• 9.2: The Matrix of a Linear Transformation
• 9.3: Properties of Linear Transformations
• 9.4: Similarity of Matrices
• Summary
• Applications
• Exercises

---

Appendices

• A: Solutions to Odd-Numbered Exercises
• B: Answers to Selected Exercises
• C: Mathematical Induction
• D: Further Topics in Matrix Algebra
• E: Properties of Determinants

---

Index

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