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Linear Algebra With Applications

Linear Algebra With Applications

Linear Algebra With Applications

Linear Algebra With Applications is a comprehensive textbook designed for students studying linear algebra at the undergraduate level. This textbook covers all the essential topics of linear algebra, including vector spaces, matrices, determinants, eigenvalues, and eigenvectors. It also includes a wide range of applications of linear algebra in various fields such as engineering, physics, and economics.

The book is written in a clear and concise manner, making it easy for students to understand the concepts and apply them to real-world problems. Each chapter includes numerous examples and exercises to help students practice and reinforce their understanding of the material. The book also includes a chapter on computational techniques, providing students with the necessary tools to solve complex problems using technology.

Linear Algebra With Applications is authored by renowned mathematicians and educators, ensuring the accuracy and quality of the content. The book is available in both print and digital formats, making it accessible to students from all backgrounds. With its comprehensive coverage and practical approach, Linear Algebra With Applications is an essential resource for any student studying linear algebra.

Visit our website at http://vedibooks.com/products/linear-algebra-with-applications to learn more and purchase your copy today.

9781292354866

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Table of Content

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

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