Linear Algebra with Applications 10th Edition by Steve J Leon, Lisette De Pillis ISBN 9780135240960 0135240964

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Product details:
ISBN 10: 0135240964
ISBN 13: 9780135240960
Author: Steve J Leon, Lisette De Pillis

Linear Algebra with Applications 10th Edition 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

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

Chapter 3 Vector Spaces

3.1 Definition and Examples

Euclidean Vector Spaces

The Vector Space ℝm×n

Vector Space Axioms

The Vector Space C[a,b]

The Vector Space Pn

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 Pn

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 ℝm

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

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 5.1Exercises

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 ℝm×n

The Vector Space C[a, b]

The Vector Space Pn

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

Chapter 6 Eigenvalues

6.1 Eigenvalues and Eigenvectors

Geometric Visualization of Eigenvalues and Eigenvectors

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 Lower 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

Critical Loads for a Beam

Diagonalizable and Defective Matrices

Application: 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

The IEEE Standard 754 Floating-Point Representation

Loss of Accuracy and Instability

Section 7.1 Exercises

7.2 Gaussian Elimination

Gaussian Elimination without Interchanges

Using the 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 Orthogonal Transformations

Householder Transformations

Remarks

Operation Count

Rotations and Reflections

Operation Count

The QR Factorization for Solving General Linear Systems

Section 7.5 Exercises

7.6 The Eigenvalue Problem

The Power Method

Deflation

Reduction to Hessenberg Form

QR Algorithm

Remarks

Section 7.6 Exercises

7.7 Least Squares Problems

Normal Equations

Modified Gram–Schmidt Method for Solving Least Squares Problems

The Householder QR Factorization

The Pseudoinverse

Bidiagonalization

The 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

Sensitivity of Linear Systems

Sensitivity of Eigenvalues

Householder Transformations

Rotations and Reflections

Singular Value Decomposition

Gerschgorin Circles

Distribution of Condition Numbers and Eigenvalues of Random Matrices

Chapter Test A True or False

Chapter Test B

Chapter 8 Canonical Forms

8.1 Nilpotent Operators

Section 8.1 Exercises

8.2 The Jordan Canonical Form

Section 8.2 Exercises

Appendix: Matlab

The MATLAB Desktop Display

Basic Data Elements

Submatrices

Generating Matrices

Matrix Arithmetic

Addition and Multiplication of Matrices

Backslash or Matrix Left Division

Exponentiation

MATLAB Functions

Programming Features

M-files

Script Files

Function Files

The MATLAB Path

Relational and Logical Operators

Columnwise Array Operators

Graphics

Symbolic Toolbox

Help Facility

Conclusions

Bibliography

A Linear Algebra and Matrix Theory

B Applied and Numerical Linear Algebra

C Books of Related Interest

Answers to Selected Exercises

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Tags: Steve J Leon, Lisette De Pillis, Linear Algebra, Applications