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

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Chapter Test B

2. Determinants

2.1 The Determinantof a Matrix

2.2 Properties ofDeterminants

2.3 Additional Topicsand Applications

MATLAB Exercises

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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

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Chapter Test B

4. LinearTransformations

4.1 Definition andExamples

4.2 MatrixRepresentations of Linear Transformations

4.3 Similarity

MATLAB Exercises

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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 GramSchmidtOrthogonalization Process

5.7 OrthogonalPolynomials

MATLAB Exercises

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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

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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

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8. Canonical Forms

8.1 Nilpotent Operators

8.2 The JordanCanonical Form

Appendix: MATLAB

Bibliography

Answers to SelectedExercises

Index