Linear Algebra with Applications, Global Edition (10^th Ed.)

This book is for junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite.

This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualisation play in understanding linear algebra.

1. Matrices andSystems of Equations 

1.1 Systems of LinearEquations 

1.2 Row Echelon Form

1.3 Matrix Arithmetic

1.4 Matrix Algebra

1.5 ElementaryMatrices

1.6 PartitionedMatrices

MATLAB Exercises

Chapter Test A — Trueor False

Chapter Test B

2. Determinants

2.1 The Determinantof a Matrix

2.2 Properties ofDeterminants

2.3 Additional Topicsand Applications

MATLAB Exercises

Chapter Test A — Trueor False

Chapter Test B

3. Vector Spaces

3.1 Definition andExamples

3.2 Subspaces

3.3 LinearIndependence

3.4 Basis and Dimension

3.5 Change of Basis

3.6 Row Space andColumn Space

MATLAB Exercises

Chapter Test A — Trueor False

Chapter Test B

4. LinearTransformations

4.1 Definition andExamples

4.2 MatrixRepresentations of Linear Transformations

4.3 Similarity

MATLAB Exercises

Chapter Test A — Trueor False

Chapter Test B

5. Orthogonality

5.1 The ScalarProduct in Rⁿ

5.2 OrthogonalSubspaces

5.3 Least SquaresProblems

5.4 Inner ProductSpaces

5.5 Orthonormal Sets

5.6 The Gram–SchmidtOrthogonalization Process

5.7 OrthogonalPolynomials

MATLAB Exercises

Chapter Test A — Trueor False

Chapter Test B

6. Eigenvalues

6.1 Eigenvalues andEigenvectors

6.2 Systems of LinearDifferential Equations

6.3 Diagonalization

6.4 HermitianMatrices

6.5 The SingularValue Decomposition

6.6 Quadratic Forms

6.7 Positive DefiniteMatrices

6.8 NonnegativeMatrices

MATLAB Exercises

Chapter Test A — Trueor False

Chapter Test B

7. Numerical LinearAlgebra

7.1 Floating-PointNumbers

7.2 GaussianElimination

7.3 Pivoting Strategies

7.4 Matrix Norms andCondition Numbers

7.5 OrthogonalTransformations

7.6 The EigenvalueProblem

7.7 Least SquaresProblems

7.8 Iterative Methods

MATLAB Exercises

Chapter Test A — Trueor False

Chapter Test B

8. Canonical Forms

8.1 Nilpotent Operators

8.2 The JordanCanonical Form

Appendix: MATLAB

Bibliography

Answers to SelectedExercises

Index

· Extensive applications of linear algebra concepts to avariety of real-world situations are provided. Students learn how theories andconcepts of linear algebra can help solve modern-day problems.

· Abundant computer exercises—more extensive thanany other linear algebra book available—help students visualize and discoverlinear algebra and allow them to explore more realistic applications that aretoo computationally intensive to work out by hand. These exercises also givestudents experience in performing matrix computations.

· Worked-out examples illustrate new concepts, makingthe material less abstract and helping students quickly build theirunderstanding.

· Two chapter testsfor every chapter helpstudents study for exams and get the practice they need to master the material.

A comprehensiveMATLAB^® appendix gives users all the information theyneed to use the latest version of MATLAB.