Linear Algebra with Applications 10th Edition by Lisette de Pillis, Steve Leon ISBN 0136746055 9780136746058

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ISBN 10: 0136746055
ISBN 13: 9780136746058
Author: Lisette de Pillis, Steve Leon

This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. A thorough and accessible introduction to linear algebra, delivered digitally. The new 10th Edition of Linear Algebra with Applications continues to encourage a challenging and broad understanding of the subject. For this edition, Steve Leon – one of the leading figures in the use of technology for linear algebra – is joined by new co-author Lisette de Pillis of Harvey Mudd College, who brings her passion for teaching and solving real-world problems to this revision. Key to the 10th Edition was transforming from a primarily print-based resource to a digital learning tool. The eText is packed with content and tools, such as interactive figures, that help bring course content to life for students and augment instruction. This change in format supports the authors’ hallmark – using modern practical application to make key concepts tangible and demonstrating how mathematics is used in the real world. Each chapter contains integrated worked examples, practical applications, computer exercises, and chapter tests.  The important roles played by geometry and visualization in understanding linear algebra are emphasized. For sophomore-level or junior/senior-level first courses in linear algebra; assumes calculus as a prerequisite. Pearson eText allows educators to easily share their own notes with students so they see the connection between their reading and what they learn in class – motivating them to keep reading, and keep learning. Portable access lets students study on the go, even offline. And, student usage analytics offer insight into how students use the eText, helping educators tailor their instruction. NOTE: This ISBN is for the Pearson eText access card. For students purchasing this product from an online retailer, Pearson eText is a fully digital delivery of Pearson content and should only be purchased when required by your instructor. In addition to your purchase, you will need a course invite link, provided by your instructor, to register for and use Pearson eText. 0135181631 / 9780135181638 PEARSON ETEXT LINEAR ALGEBRA WITH APPLICATIONS — ACCESS CARD, 10/e 

Linear Algebra with Applications 10th Table of contents:

Chapter 1: Matrices and Systems of Equations

1.1 Systems of Linear Equations

• 2×2 Systems

• Equivalent Systems

• n×n Systems

• Section 1.1 Exercises

1.2 Row Echelon Form

• Overdetermined Systems

• Underdetermined Systems

• Reduced Row Echelon Form

• Homogeneous Systems

• Section 1.2 Exercises

1.3 Matrix Arithmetic

• Matrix Notation

• Vectors

• Equality

• Scalar Multiplication

• Matrix Addition

• Matrix Multiplication and Linear Systems

• Matrix Multiplication

• Notational Rules

• The Transpose of a Matrix

• Section 1.3 Exercises

1.4 Matrix Algebra

• Algebraic Rules

• Notation

• The Identity Matrix

• Matrix Inversion

• Note

• Algebraic Rules for Transposes

• Symmetric Matrices and Networks

• Section 1.4 Exercises

1.5 Elementary Matrices

• Equivalent Systems

• Elementary Matrices

• Diagonal and Triangular Matrices

• Triangular Factorization

• Section 1.5 Exercises

1.6 Partitioned Matrices

• Block Multiplication

• Outer Product Expansions

• Section 1.6 Exercises

• Chapter 1 Exercises

• MATLAB Exercises

• Chapter Test A: True or False

• Chapter Test B

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Chapter 2: Determinants

2.1 The Determinant of a Matrix

• Section 2.1 Exercises

2.2 Properties of Determinants

• Row Operation I

• Row Operation II

• Row Operation III

• Note

• Main Results

• Section 2.2 Exercises

2.3 Additional Topics and Applications

• The Adjoint of a Matrix

• Cramer’s Rule

• Reference

• The Cross Product

• Section 2.3 Exercises

• Chapter 2 Exercises

• MATLAB Exercises

• Chapter Test A: True or False

• Chapter Test B

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Chapter 3: Vector Spaces

3.1 Definition and Examples

• Euclidean Vector Spaces

• The Vector Space ℝ^m×n

• Vector Space Axioms

• The Vector Space C[a, b]

• The Vector Space P_n

• Additional Properties of Vector Spaces

• Section 3.1 Exercises

3.2 Subspaces

• The Null Space of a Matrix

• The Span of a Set of Vectors

• Spanning Set for a Vector Space

• Linear Systems Revisited

• Section 3.2 Exercises

3.3 Linear Independence

• Geometric Interpretation

• Theorems and Examples

• Vector Spaces of Functions

• The Vector Space P_n

• The Vector Space C⁽ⁿ⁻¹⁾[a, b]

• Section 3.3 Exercises

3.4 Basis and Dimension

• Standard Bases

• Section 3.4 Exercises

3.5 Change of Basis

• Changing Coordinates in ℝ²

• Changing Coordinates

• Change of Basis for a General Vector Space

• Section 3.5 Exercises

3.6 Row Space and Column Space

• Linear Systems

• The Column Space

• Note

• Section 3.6 Exercises

• Chapter 3 Exercises

• MATLAB Exercises

• Chapter Test A: True or False

• Chapter Test B

---

Chapter 4: Linear Transformations

4.1 Definition and Examples

• Notation

• Linear Operators on ℝ²

• Linear Transformations from ℝⁿ to ℝ^m

• Linear Transformations from V to W

• The Image and Kernel

• Section 4.1 Exercises

4.2 Matrix Representations of Linear Transformations

• Section 4.2 Exercises

4.3 Similarity

• Section 4.3 Exercises

• Chapter 4 Exercises

• MATLAB Exercises

• Chapter Test A: True or False

• Chapter Test B

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Chapter 5: Orthogonality

5.1 The Scalar Product in ℝⁿ

• The Scalar Product in ℝ² and ℝ³

• Scalar and Vector Projections

• Notation

• Orthogonality in ℝⁿ

• Section 5.1 Exercises

5.2 Orthogonal Subspaces

• Note

• Remarks

• Fundamental Subspaces

• Section 5.2 Exercises

5.3 Least Squares Problems

• Least Squares Solutions of Overdetermined Systems

• Section 5.3 Exercises

5.4 Inner Product Spaces

• Definition and Examples

• The Vector Space ℝⁿ

• The Vector Space ℝ^m×n

• The Vector Space C[a, b]

• The Vector Space P_n

• Basic Properties of Inner Product Spaces

• Observations

• Norms

• Section 5.4 Exercises

5.5 Orthonormal Sets

• Orthogonal Matrices

• Permutation Matrices

• Orthonormal Sets and Least Squares

• Approximation of Functions

• Approximation by Trigonometric Polynomials

• Section 5.5 Exercises

5.6 The Gram–Schmidt Orthogonalization Process

• The Modified Gram–Schmidt Process

• Section 5.6 Exercises

5.7 Orthogonal Polynomials

• Orthogonal Sequences

• Classical Orthogonal Polynomials

• Legendre Polynomials

• Chebyshev Polynomials

• Jacobi Polynomials

• Hermite Polynomials

• Laguerre Polynomials

• Section 5.7 Exercises

• Chapter 5 Exercises

• MATLAB Exercises

• Chapter Test A: True or False

• Chapter Test B

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Chapter 6: Eigenvalues

6.1 Eigenvalues and Eigenvectors

• Geometric Visualization

• Finding Eigenvalues and Eigenvectors

• Complex Eigenvalues

• The Product and Sum of the Eigenvalues

• Similar Matrices

• Section 6.1 Exercises

6.2 Systems of Linear Differential Equations

• Complex Eigenvalues

• Higher-Order Systems

• Section 6.2 Exercises

6.3 Diagonalization

• Remarks

• The Exponential of a Matrix

• Section 6.3 Exercises

6.4 Hermitian Matrices

• Complex Inner Products

• Hermitian Matrices

• The Real Schur Decomposition

• Normal Matrices

• Section 6.4 Exercises

6.5 The Singular Value Decomposition

• Observations

• Visualizing the SVD

• Numerical Rank and Low-Rank Approximations

• Section 6.5 Exercises

6.6 Quadratic Forms

• Conic Sections

• Optimization: An Application to the Calculus

• Section 6.6 Exercises

6.7 Positive Definite Matrices

• Section 6.7 Exercises

6.8 Nonnegative Matrices

• Section 6.8 Exercises

• Chapter 6 Exercises

• MATLAB Exercises

• Applications:

  • Critical Loads for a Beam

  • Diagonalizable and Defective Matrices

  • Sex-Linked Genes

  • Similarity

  • Hermitian Matrices

  • Optimization

  • Positive Definite Matrices

• Chapter Test A: True or False

• Chapter Test B

---

Chapter 7: Numerical Linear Algebra

7.1 Floating-Point Numbers

• IEEE 754 Standard

• Loss of Accuracy and Instability

• Section 7.1 Exercises

7.2 Gaussian Elimination

• Without Interchanges

• Triangular Factorization to Solve Ax = b

• Operation Count

• Section 7.2 Exercises

7.3 Pivoting Strategies

• Gaussian Elimination with Interchanges

• Remarks

• Partial Pivoting

• Section 7.3 Exercises

7.4 Matrix Norms and Condition Numbers

• Matrix Norms

• Subordinate Matrix Norms

• Condition Numbers

• Section 7.4 Exercises

7.5 Orthogonal Transformations

• Elementary and Householder Transformations

• Operation Count

• Rotations and Reflections

• QR Factorization

• Section 7.5 Exercises

7.6 The Eigenvalue Problem

• Power Method

• Deflation

• Hessenberg Reduction

• QR Algorithm

• Remarks

• Section 7.6 Exercises

7.7 Least Squares Problems

• Normal Equations

• Modified Gram–Schmidt Method

• Householder QR Factorization

• Pseudoinverse

• Bidiagonalization

• Golub–Reinsch Algorithm

• Section 7.7 Exercises

7.8 Iterative Methods

• Matrix Splittings

• Jacobi Iteration

• Gauss–Seidel Iteration

• Section 7.8 Exercises

• Chapter 7 Exercises

• MATLAB Exercises

• Topics:

  • Sensitivity of Systems and Eigenvalues

  • Householder Transforms

  • SVD

  • Gerschgorin Circles

  • Random Matrix Theory

• Chapter Test A: True or False

• Chapter Test B

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Chapter 8: Canonical Forms

8.1 Nilpotent Operators

• Section 8.1 Exercises

8.2 The Jordan Canonical Form

• Section 8.2 Exercises

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Appendix: MATLAB

• The MATLAB Desktop

• Basic Data Types

• Submatrices

• Generating Matrices

• Matrix Arithmetic

• Matrix Division and Exponentiation

• MATLAB Functions

• Programming Features:

  • M-files

  • Script vs Function Files

  • MATLAB Path

• Operators

• Graphics

• Symbolic Toolbox

• Help System

• Conclusions

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Bibliography

• A. Linear Algebra and Matrix Theory

• B. Applied and Numerical Linear Algebra

• C. Books of Related Interest

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Tags: Lisette de Pillis, Steve Leon, Linear Algebra