Linear Algebra with Applications, Global Edition

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 GramSchmidtOrthogonalization 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