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Linear Algebra and Its Applications 4th Edition, (Ebook PDF)

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Linear Algebra and Its Applications 4th Edition, (Ebook PDF) – Digital Instant Dowload.

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Linear Algebra and Its Applications 4th Edition, (Ebook PDF) – Digital Instant Dowload.

Product details:

ISBN-10 ‏ : ‎ 0321385179
ISBN-13 ‏ : ‎ 978-0321385178
Author: David C. Lay (Author)

Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick 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. Since they are fundamental to the study of linear algebra, students’ understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete Rⁿ setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.

Table contents:

ch. 1 Linear Equations in Linear Algebra

1.1. Systems of Linear Equations

1.2. Row Reduction and Echelon Forms

1.3. Vector Equations

1.4. The Matrix Equation Ax = b

1.5. Solution Sets of Linear Systems

1.6. Applications of Linear Systems

1.7. Linear Independence

1.8. Introduction to Linear Transformations

1.9. Matrix of a Linear Transformation

1.10. Linear Models in Business, Science, and Engineering

Supplementary Exercises

Glossary Checklist

ch. 2 Matrix Algebra

2.1. Matrix Operations

2.2. The Inverse of a Matrix

2.3. Characterization of Invertible Matrices

2.4. Partitioned Matrices

2.5. Matrix Factorizations

2.6. The Leontief Input-Output Model

2.7. Applications to Computer Graphics

2.8. Subspaces of Rn

2.9. Dimension and Rank

Supplementary Exercises

Glossary Checklist

ch. 3 Determinants

3.1. Introduction to Determinants

3.2. Properties of Determinants

3.3. Cramer’s Rule, Volume and Linear Transformations

Glossary Checklist

ch. 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. Coordinate Systems

4.5. The Dimension of a Vector Space

4.6. Rank

4.7. Change of Basis

4.8. Applications to Difference Equations

4.9. Applications to Markov Chains

Glossary Checklist

ch. 5 Eigenvalues and Eigenvectors

5.1. Eigenvectors and Eigenvalues

5.2. The Characteristic Equation

5.3. Diagonalization

5.4. Eigenvectors and Linear Transformations

5.5.Complex Eigenvalues

5.6. Discrete Dynamical Systems

5.7. Applications to Differential Equations

5.8. Iterative Estimates for Eigenvalues

Glossary Checklist

ch. 6 Orthogonality and Least Squares

6.1. Inner Product, Length, and Orthogonality

6.2. Orthogonal Sets

6.3. Orthogonal Projections

6.4. The Gram-Schmidt Process

6.5. Least-Squares Problems

6.6. Applications to Linear Models

6.7. Inner Product Spaces

6.8. Applications of Inner Product Spaces

Glossary Checklist

ch. 7 Symmetric Matrices and Quadratic Forms

7.1. Diagonalization of Symmetric Matrices

7.2. Quadratic Forms

7.3. Constrained Optimization

7.4. The Singular Value Decomposition

7.5. Applications to Image Processing and Statistics

Supplementary Exercises

Glossary Checklist

ch. 8 The Geometry of Vector Spaces

8.1. Affine Combinations

8.2. Affine Independence

8.3. Convex Combinations

8.4. Hyperplanes

8.5. Polytopes

8.6. Curves and Surfaces

Title tag:

1. Linear Algebra and Its Applications 4th Edition – Essential Textbook for Mathematics Students
2. Master Key Concepts with Linear Algebra and Its Applications 4th Edition – Comprehensive Guide
3. Dive Deep into Vector Spaces with Linear Algebra and Its Applications 4th Edition