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